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Review ArticleOpen Access

Theoretical Investigation of Harmful Information Propagation Using Physical Properties of Graphene and TeNPs: Sociophysical Approach Volume 60- Issue 1

Yasuko Kawahata*

  • Faculty of Sociology, Rikkyo University, Japan

Received: December 07, 2024; Published: December 17, 2024

*Corresponding author: Yasuko Kawahata, Faculty of Sociology, Rikkyo University, 3-34-1 Nishi-Ikebukuro,Toshima-ku, Tokyo, 171-8501, Japan

DOI: 10.26717/BJSTR.2024.60.009385

Abstract PDF

ABSTRACT

This study is an attempt to apply first-principles calculations in materials science, especially density functional theory (DFT) methods and physical models of telluric nanoparticles (TeNPs) and graphene, to social physics. In the recent digital society, the proliferation of harmful information has caused a wide range of problems from individual mental health to social fragmentation. In this study, we utilize the fast electronic conduction properties of graphene and the localization properties of TeNPs to model the dual nature of the rapid diffusion of harmful information and its disfiguration. From the simulation results, we analyze the dynamics of information propagation as the network size changes, and in particular, we clarify the interaction between the information immobilization effect of the TeNPs structure and the diffusion enhancement effect of the graphene structure. Numerical experiments using the SIR model and the threshold model were conducted to quantitatively evaluate the structure dependence in the suppression of diffusion of harmful information. This study provides a new perspective of understanding social phenomena through a physical approach and suggests the importance of preventive and structural approaches in countermeasures against harmful information. Future issues include validation of the model using real data and generalization of the theory through comparison with other material models.

Keywords: Sociophysics; First-principles Calculations; Density Functional Theory; Harmful Information Diffusion; Telluric Nanoparticles; Graphene; Doomskilling

Abbreviations: JSPS: Japan Society for the Promotion of Science; TeNPs: Ttellurium-based Nanoparticles; TDLDA: Time-Dependent Local Density Approximation; DFT: Density Functional Theory; TCIC: Time-Competitive Independent Cascade

Introduction

This study serves as a preliminary attempt to integrate first-principles computational methodologies from materials science—particularly density functional theory (DFT)—alongside the physical modeling of tellurium-based nanoparticles (TeNPs) and graphene, into an exploratory framework for social physics. Rapid advancements in information technology have led us into an era in which vast amounts of data are disseminated instantaneously. Within this context, issues such as hate speech, fabricated news, information manipulation, and the lack of digital ethics have become increasingly manifest. These challenges significantly affect individuals, societies, and nation-states, threatening the bedrock of democracy and fundamental human rights [1-6]. Moreover, modeling how noxious information—such as hate speech and disinformation—becomes rigidly entrenched within large-scale datasets remains a formidable task. Numerous cases exemplify the extensive proliferation of detrimental content. In the contemporary digital environment, hostile materials and hate speech are widely acknowledged as grave types of harmful information. They not only violate personal rights, foster social fragmentation, and destabilize democratic foundations, but also pose severe threats to the cohesion of entire communities. In the present discussion, hate speech and fake news are collectively addressed as “harmful information.” Recently, the spread of hazardous content and hate speech triggering social polarization has surged online, stimulated by events including the COVID-19 pandemic, large-scale disasters, regional conflicts, and major electoral campaigns.

Such harmful materials reach individuals directly through digital media, inducing societal disarray, swaying public opinion, and exposing communities to serious risks in terms of public health and mental well-being. The phenomenon of “doomscrolling,” characterized by excessive consumption of negative news, correlates with heightened anxiety and stress. Furthermore, indirect exposure to others’ traumatic experiences through media can result in secondary trauma [7- 13]. First, this introduction will organize the qualitative perspectives on harmful information, serving as a conceptual foundation for the subsequent analysis.

The Detriment of Fake News [7-9]

Fake news inflicts harm upon society in the following ways:
• Incitement of social unrest through the intentional distribution of falsehoods
• Distortion of democratic procedures and interference in electoral activities
• Erosion of trust in media outlets and governmental institutions
• Intensification of social divisions and exacerbation of hostilities

The Harm of Hate Speech [12,13]

Hate speech generates adverse effects in multiple forms:

• Psychological damage inflicted on specific individuals or groups
• Reinforcement of discrimination and prejudicial attitudes
• Splintering of communities and deepening of conflicts
• Increased likelihood of offline violence
Taking these elements into consideration, harmful information in the digital era can be described as follows:

Definition and Characteristics of Harmful Information

Harmful content in a digital setting typically exhibits:

a. Intentionality: Created and disseminated to achieve particular objectives
b. Detrimental Impact: Imposes tangible harm on individuals or social structures
c. High Diffusivity: Rapidly proliferates through online platforms
d. Persistence: Once circulated, complete removal is exceedingly difficult

Moreover, the mechanisms driving dissemination are significantly influenced by algorithmic factors.

Mechanisms Behind the Spread of Harmful Information

a. Algorithmic Dynamics

• Ranking systems prioritizing engagement
• Promotion of echo chambers
• Amplification of emotional reactions

b. Factors Facilitating Distribution

• Reduced restraint due to online anonymity
• Instantaneous propagation through sharing functionalities
• Chain-like diffusion across multiple platforms These elements interact in complex ways, as shown below.

Interrelated Causes of Harmful Content

Building on the above, it is possible to infer that harmful content poses multifaceted risks to society.Societal Harms Stemming from Harmful Information Individual-Level Consequences

a. Psychological Harm

• Heightened anxiety and stress
• Declines in self-esteem
• Potential trauma induction

b. Cognitive Detriments

• Reduced decision-making ability
• Reinforcement of cognitive biases
• Information overload leading to fatigue

Evaluating these individual-level effects highlights their implications for mental health.

Specific Impacts on Mental Health [13]

In Japan, for instance, a survey by the Ministry of Internal Affairs and Communications reveals that, among those who encountered coronavirus-related harmful content, 58.9% recognized it as false. However, with regard to domestic political content, only 18.8% identified it as fabricated [14]. Another study indicates that approximately 75% of respondents believed harmful information, and the most common method of dissemination was direct conversation with friends, acquaintances, and family [15]. Furthermore, harmful content on social media platforms tends to spread at a swifter pace and reach more users than factual news. Such misinformation can spark social disorder and produce negative repercussions on both public health and mental well-being. Of particular concern is the severe toll that this propagation of harmful information can exact on mental health. Considered on a global scale, exposure to violent news on social networks has the potential to induce trauma in those who consume it.

These instances underline that harmful information constitutes a grave contemporary challenge, necessitating effective countermeasures. According to McLaughlin, Gotlieb, and Mills [16], “doomscrolling” signifies a behavioral pattern characterized by descending into a negative news cycle [16]. Their study reveals that individuals who frequently engaged with social media during the pandemic were more prone to experiencing excessive anxiety and depressive symptoms. In particular, those with pre-existing social anxiety disorders or a history of depression faced heightened risks of exacerbation due to doomscrolling. The investigation identified an “information overload” tendency, wherein participants continued searching for related content rather than avoiding specific news. Such behavior, as the volume of information grows, tends to intensify psychological stress. In another investigation, Shabahang and Nguyen [17] clarified the longterm ramifications of doomscrolling [17]. Their findings indicate that extensive consumption of negative news via social media correlates strongly with deteriorations in subjective mental health assessments and diminished perceptions of well-being. Specifically, about 78% of respondents reported experiencing fatigue and stress following periods of doomscrolling, factors which were further linked to sleep disturbances and feelings of social isolation. While the authors propose mitigation strategies such as limiting information exposure and employing time-management tools, they also acknowledge the difficulty of achieving complete prevention. Both studies highlight that harmful information often serves as a catalyst for doomscrolling. In particular, misinformation that amplifies a sense of crisis readily captures viewers’ attention and can trigger excessive news consumption. These behaviors not only escalate anxiety without leading to realistic solutions but ultimately culminate in psychological exhaustion and a sense of helplessness.

A critical lesson emerging from this body of research is the indispensable need for individual-level behavioral modifications. Mc- Laughlin and colleagues suggest that imposing restrictions on social media usage and selecting credible sources can help minimize the impact of doomscrolling. Conversely, Shabahang and colleagues advocate that technology companies refine their algorithms to balance the flow of information reaching users. These findings illuminate the reciprocal influence between harmful content and doomscrolling, which collectively aggravates mental health detriments. Addressing this issue demands coordinated efforts from individuals and society at large. Although the interplay between harmful information and doomscrolling, as well as the escalation of mental health disorders, can be viewed as a kind of natural phenomenon, fully encapsulating their myriad patterns remains challenging. Moreover, as large-scale and long-term dissemination of detrimental content unfolds, tracing its diffusion pathways and initial infection routes becomes increasingly difficult. In such scenarios, hypotheses, extensive computational simulations, and the insights they yield may be necessary.

Against this backdrop, we consider adapting first-principles computational techniques—originally developed in materials physics for large-scale simulations and structure detection—to model both the fixation and rapid spread of harmful information. First-principles methods do not rely on empirical parameters; instead, they derive material properties directly from quantum mechanics [18], making them well-suited for predicting the characteristics of unfamiliar systems and the networks linking individual “particles” of information [19]. Indeed, current large-scale, complex problems often require expansive computational resources combined with first-principles approaches [20-22]. Here, we aim to exploit the physical properties of Te-based nanoparticles (TeNPs) and graphene as a means to model the duality of harmful information dissemination—its entrenchment and its rapid spread—and to glean insights through simulation. Admittedly, this endeavor is highly exploratory and theoretical. From an educational standpoint, this study can be regarded as an attempt to apply first-principles calculations and the framework of sociophysics to analyze the dissemination of harmful content.

a. Advances in Sociophysics

Sociophysics is an interdisciplinary field that employs theoretical constructs and methodologies from physics to examine social phenomena. By applying tools from statistical physics to the social sciences, it seeks to elucidate the dynamics and emergent patterns within complex societal systems. Galam [23-25] adapted the Ising model, originally formulated in physics to represent spin interactions in magnetic materials, to analyze electoral processes and opinion formation. The Ising model considers individual spins with binary states, and their interactions determine the system’s overall energy. By applying this model to social contexts, Galam revealed how pairwise interactions among individuals influence collective decision-making. Sznajd-Weron and Sznajd [26,27] introduced the Sznajd model, also inspired by magnetic systems. In this approach, pairs of individuals holding the same opinion influence those around them, simulating opinion propagation and selforganization processes. This model is crucial for understanding the mechanisms underpinning information dissemination and the spread of social influence. In addition, a range of other opinion dynamics models—such as the Potts model and the Bounded Confidence Model [28]—have been proposed, each offering insights into how collective patterns arise from individual interactions.

b. Progress in Opinion Dynamics

Recent research by Ishii and Kawahata [29-32] has introduced innovative theoretical perspectives on online opinion formation and polarization. They particularly emphasize the role of trust and distrust in shaping belief formation [33,34], thereby advancing our understanding of consensus-building mechanisms in digital environments [35]. Classical theoretical foundations in opinion dynamics include contributions by French [36], Harary [37], Abelson [38], and DeGroot [39]. Additionally, Noelle-Neumann’s spiral of silence theory [40] has served as a critical conceptual basis for comprehending the processes that shape public opinion.

c. First-Principles Calculations and Sociophysics

First-principles calculations are methodologies that derive a material’s properties directly from the fundamental laws of quantum mechanics, without relying on empirical parameters. A representative framework within this category is Density Functional Theory (DFT), which computes the ground-state energy of a system based on its electron density, thereby enabling a detailed examination of many- body interactions.

This approach exhibits strong conceptual affinity with the bounded confidence models proposed by Bronson [41] and Hegselmann et al. [28,41,42], particularly in regard to establishing thresholds and boundary conditions that dictate interactions in opinion formation processes. It also allows for the potential advancement of nonlinear consensus formation models proposed by Krause [43,44] as well as the agent-based interaction models developed by Deffuant and colleagues [45]. The continuous opinion dynamics framework introduced by Weisbuch et al. [46] shares analogous features with the continuous variation of electron density in first-principles computations. In addition, Dittmer’s [47] exploration of consensus formation under bounded confidence conditions provides valuable insights into the role of boundary constraints, paralleling the treatment of systems within first-principles approaches.

d. Hypotheses and Objectives of the Present Study

Building on these prior findings, we draw upon the convergence theorems of iterative averaging in consensus formation by Chatterjee and Seneta [48], as well as Wagner’s [49] model of rational collective decision-making. Moreover, Lehrer’s [50] theoretical perspective on social consensus formation and Chatterjee’s [51] extremal limit theorems on consensus further contribute to the theoretical underpinnings of this research. Recent empirical results by Bail et al. [52], demonstrating that exposure to adversarial perspectives on social media enhances political polarization, and the analyses by Tsubokura et al. [53] on scientific communication during crises hint at the practical applicability of our proposed approach. In light of this theoretical foundation, our investigation sets out three primary objectives. First, we aim to leverage the physical models of tellurium-based nanoparticles (TeNPs) and graphene to analyze the structure and dynamics of social networks. By drawing on these material models, it becomes feasible to mathematically characterize patterns of information flow and interactions within social networks. Second, through the use of first-principles methodologies, we intend to examine in detail the diffusion patterns of detrimental information inherent in large-scale datasets. This perspective permits a quantitative understanding of the routes of dissemination, the velocity of spread, and the scope of influence that harmful content can exert. Third, from a sociophysical standpoint, we seek to elucidate the underlying mechanisms governing information transmission. By doing so, we hope to clarify how messages propagate within social networks and how such processes affect individual and group behavior. These interconnected aims, when viewed comprehensively, facilitate a deeper grasp of the phenomena behind information diffusion.

i. Potential Application of First-Principles Calculations and DFT to Sociophysics:

Because first-principles methods compute system properties directly from fundamental principles without relying on empirical parameters, their models are both stringent and universal. Specifically, Density Functional Theory (DFT) achieves a balance between computational efficiency and accuracy by treating many-body effects in terms of electron density functions.

e. DFT’s Large-Scale Data Processing Capability and Its Applicability

For large-scale systems, the novel potential-based conjugate gradient algorithm for order-N self-consistent total energy computations developed by Gonze [54] serves as a crucial foundation. Eliminating the explicit use of wavefunctions, this technique enables efficient calculations in extensive systems. Regarding linear scaling methods, Vasiliev et al. [55] have implemented linear response theory within the time-dependent local density approximation (TDLDA), establishing an efficient computational methodology for sizable systems. By optimizing grid dimensions and the sparsity of the Hamiltonian matrix, this approach achieves high-precision results at controlled computational costs. For the thorough depiction of many-body interactions, the work of Mackrodt et al. [56] on a variety of single-particle Hamiltonians offers a reference point. Their research clarifies the influence of distinct exchange terms on the characteristics of a system, insights that can be extended to depict intricate interactions within social structures. Additionally, the machine learning-based density functional approximation methods introduced by Kalita et al. [57] present new avenues for enhancing computational efficiency and accuracy. Furthermore, the nonlocal atomic pseudopotentials developed by Zhu et al. [18] offer a suggestive model for representing both localized and nonlocal interactions within social networks. These theoretical advances open up promising possibilities for large-scale data analysis in sociophysics. In particular, the incorporation of microscopic interaction effects that traditional approaches might overlook can now be integrated into analyses of information dissemination and opinion formation processes within social networks.

Theoretical Considerations on a Harmful Information Model Utilizing Graphene and Tenps

This paper contemplates the theoretical validity of a harmful information diffusion model informed by the physical properties of graphene and tellurium-based nanoparticles (TeNPs). Drawing on the knowledge gained from Vasiliev et al. [55] regarding first-principles DFT calculations, we compare and contrast our proposed framework with analogous materials to clarify both its distinctive features and its inherent limitations.

f. Rationale for Employing Graphene and TeNPs

The diffusion of harmful information displays a dual aspect: propagation and localization. To represent these attributes using a physical model, we follow the lead of Mackrodt et al. [56], applying insights from DFT-based research to exploit the electron properties of graphene and TeNPs. Graphene, with its massless Dirac electrons that allow for rapid carrier motion, is well-suited for modeling high-speed information dispersal, especially in light of the density functional approximations proposed by Kalita et al. [57]. Conversely, TeNPs, where electrons tend to be more localized, can capture the fixation and retention of information, leveraging the order-N selfconsistent computational strategy by Gonze [54].

i. Formulating the Fundamental Concepts: Following Hegselmann and Krause’s [28] bounded confidence model, the fundamental equation for harmful information diffusion can be extended as:

Here, the first term D2P(r,t ) signifies the spatial dispersion of information. Drawing on the nonlocal pseudopotential approach by Zhu et al. [18], the diffusion coefficient D determines the speed and scope of content propagation. The second term α P(r,t )(1− P(r,t ) , inspired by Galam’s [24] statistical physics perspective, reflects nonlinear amplification

ii. Physical Interpretation of Localization in the TeNPs Model: Information localization can be described by extending the Sznajd-Weron and Sznajd [26] model as follows:

In this formulation, si is a site-specific variable (such as a spin variable indicating the presence or absence of information), and ni is an occupation number operator, equal to 1 if information is present and 0 otherwise. The term Jij represents the strength of interactions between sites, dictating the extent to which information propagates and correlates, while Δi is a localization energy that signifies the tendency of information to remain fixed at site i . This formalism parallels fundamental statistical mechanics models like the Ising or Hubbard models, enabling the description of localization and cluster formation in information transmission. The approach also builds on Ishii and Kawahata’s [29,30] opinion dynamics theories, employing their techniques for characterizing information localization and clusterization.

g. Comparative Analysis of Material Properties: Correspondence Between Electronic States and Information Propagation: By employing Vasiliev et al.’s [55] first-principles calculation methods, it becomes feasible to illustrate how each material’s electronic configuration aligns with distinct modes of information transmission. Drawing on Mackrodt et al.’s [52] density functional theory (DFT) analyses, graphene can serve as a proxy for high-speed spreading, TeNPs for the anchoring of content, TMDCs for selective propagation, and CNTs for directional flow.

h. Alignment with Social Phenomena

i. Modeling Information Diffusion Using a Master Equation: Building on the methods introduced by Hegselmann and Krause [28], as well as Deffuant et al. [45], the temporal evolution of information dissemination can be formulated through the following master equation:

Here, P(s,t ) denotes the probability that the system is in state s at time t , and W(s | s′ ) is the transition probability from state s′ to s. Drawing upon the opinion dynamics framework of Ishii and Kawahata [29], this equation characterizes how information moves between individuals or nodes, as well as how the entire system evolves over time. By adopting Galam’s [24] statistical physics approach, factors such as transmission speed, influential power, and credibility—social parameters essential to realistic modeling—can be integrated into the transition probabilities W(s | s′ ) .

i. Hierarchical Structure of Interactions

Referring to Tsubokura et al. [53] and DeDeo [58], the interactions driving information propagation exhibit a hierarchical structure encompassing direct interpersonal influence (local interactions), intra- community sharing (medium-range interactions), and extensive diffusion via social media or mass media channels (long-range interactions). By combining Noelle-Neumann’s [40] spiral of silence theory with Bail et al.’s [52] social media research, Figure 1 provides a visual representation of these layered modes of interaction.

Figure 1

biomedres-openaccess-journal-bjstr

j. Verification of the Theoretical Model

i. Evaluating Simulation Outcomes Through Information Entropy: Advancing Hegselmann and Krause’s [28] approach, we assess simulation outputs using the following measure of information entropy:

Here, E (t ) is the total information entropy of the system, Pi(t ) represents the probability of information being present at node i , and N is the total number of nodes. Building on the studies by Deffuant et al. [45] and Weisbuch et al. [54], this entropy quantifies the uncertainty and diversity of the information distribution. A uniform, widespread dissemination of information leads to maximal entropy.

k. Assessing the Model’s Validity

i. Theoretical Basis of Local Conservation Laws: Applying Vasiliev et al.’s [55] first-principles methodology, we can derive the following theorem: By utilizing the concept of order-N self-consistent computations introduced by Gonze [54], we establish that local conservation laws hold within the graphene-TeNP composite system:

Here, ρ is the information density and j is the information flux. Grounded in the DFT-based studies of Mackrodt et al. [56], this conservation law indicates that, within the system, the amount of information remains constant over time, neither created nor destroyed.

ii. Physical Interpretation of Experimental Observables: In line with Ishii and Kawahata’s [29,30] theories of opinion dynamics, we define an observable suitable for empirical validation:

Drawing on the machine learning approaches discussed by Kalita et al. [57], this observable quantifies the degree of correlation among nodes. Such a measure is useful for analyzing social polarization as examined by Bail et al. [52]. Key attributes of the proposed model include:

• The nonlocal pseudopotential concept by Zhu et al. [18] enables describing the dual nature of information dissemination within a single framework.

• Tsubokura et al.’s [53] empirical findings highlight the feasibility of applying this approach to large-scale systems.

• Experimental validation grounded in Galam’s [24] statistical physics perspective is achievable.

However, several issues remain open for future exploration:

a. Incorporating the notions of trust and distrust, as proposed by IshiiEtAl [34], into more complex social network structures.

b. Integrating quantum effects relevant to NoelleNeumann’s [40] spiral of silence theory.

c. Conducting more nuanced comparisons with real-world data guided by the consensus formation framework of KawahataIshii [35].

l. In-Depth Considerations on the Effectiveness of the Graphene-TeNPs Composite Model

i. Fundamental Mechanisms of Information Dissemination:Drawing on Vasiliev et al.’s [55] first-principles approach, the effectiveness of the graphene-TeNPs composite framework can be theoretically justified as follows:

Adopting Gonze’s [105] order-N self-consistent computation principles, each term is defined as:

Based on Mackrodt et al.’s [56] DFT analysis, Hgraphene characterizes the swift electronic transport within graphene, while HTeNPs represents the localized electrons and their interactions in TeNPs. Together, these terms and their coupling through Hinteraction elucidate the dual nature of information propagation—rapid and expansive in the graphene layer, localized and retained in the TeNPs domain—providing a cohesive theoretical foundation for the proposed model.

ii. Concrete Applications: Building upon Hegselmann and Krause’s [28] and Deffuant et al.’s [45] approaches, the application of the composite model can be expressed as follows:

In this equation, the final term, , adapts Gonze’s [54] self-consistent computational method to represent the capture or attenuation of information at localization centers (positions of TeNPs).

m. Rationale for Choosing the Graphene-TeNPs Composite

Model By integrating Kalita et al.’s [57] machine-learning methodology and Zhu et al.’s [18] nonlocal pseudopotential framework, the selection of the graphene-TeNPs composite model is justified on the following grounds:

a. Physical Consistency: The model naturally reconciles the seemingly conflicting characteristics of high-speed propagation and robust localization, enabling a unified representation of complex information dissemination dynamics.

b. Computational Efficiency: The relatively simple structure of the model keeps computational costs at manageable levels, making it practical for simulating large-scale systems over extended periods.

c. Model Flexibility: Parameter adjustments are straightforward, allowing adaptation to various scenarios and conditions. In particular, controlling scale dependence and the intensity of interactions provides a high degree of versatility. These properties bring the modeling approach closer to capturing the essential features of harmful information proliferation accurately and efficiently.

n. Limitations and Future Perspectives of the Model

i. Examining Theoretical Boundaries: Drawing on firstprinciples methods proposed by Gonze [54] and Vasiliev et al. [55], we derive the following theorem: [Fundamental Limitation] The graphene- TeNPs composite model is subject to intrinsic constraints described by Mackrodt et al. [56,59]:

o. Constraints on the Model

Based on Ishii and Kawahata’s [29,30] sociophysical approach, the following constraints are defined: As shown in Tsubokura et al.’s [53,59] empirical studies, these constraints indicate that real-world applicability of the model remains limited.

p. Possibilities Offered by Other Materials

a. Topological Materials: By applying Kalita et al.’s [57] machine- learning approach and incorporating topological insulators or other advanced material systems, it may be possible to enhance the controllability and robustness of information dissemination, as suggested by Bail et al. [52].

b. Building Hybrid Theories: Combining Zhu et al.’s [18] nonlocal pseudopotential methods with the trust-distrust modeling of Ishii et al. [34] opens avenues for more comprehensive theoretical frameworks. Future research should focus on the following hybrid models:

a. Enhancing multi-faceted approaches derived from Hegselmann and Krause’s [28] model

b. Pursuing empirical validation informed by NoelleNeumann’s [40] theory

c. Broadening the scope of applications through Kawahata and Ishii’s [35] methods

Through these endeavors, tackling the mechanisms underlying harmful information dissemination remains a critical challenge in the field of sociophysics.

Prior Studies

Although direct applications of graphene-based physical models to socio-economic phenomena are sparse, related research provides insightful precedents. In network science, Baraba´si and Albert [60] introduced a scale-free network model to characterize features of the internet and social networks. Meanwhile, Watts and Strogatz [61] proposed a small-world network model to elucidate the efficiency of social connectivity. As an example of applying phase transition theory to the social sciences, Kleineberg et al. [62] employed topological methods to analyze both the structure and functionality of complex networks. Recent trends have focused on computational models of information and behavior spread within social networks, as discussed by Kleinberg [63]. Conte and Giardini [64] identified four methodological approaches in computational social science, while Chopra [65] emphasized the computation of social dependencies among autonomous agents. Hegselmann and Terna [66,67] advocated agentbased modeling as a means to simulate social phenomena, and Kleinberg [68] proposed computational approaches at a global scale. Conte et al. [69] discussed the integration of computational social science with big data analysis, and Yuan [66] proposed a physical model for social networks. Regarding the influence and dissemination of harmful content, Menczer [70], Ojha et al. [71], and Xian et al. [72] investigated the mechanisms behind the spread of misinformation in social media. Roozenbeek and van der Linden [73] examined the diffusion of divisive content, and Simpson et al. [74] studied the impact of propagation speed and temporal penalties. Recent work by Taguchi et al. [75], Kadakia et al. [76], and Marecos et al. [77] proposed policy-oriented approaches to counter harmful information. These studies underscore the importance of integrating physical and social science methodologies. Ishii and Kawahata’s [29,30] opinion dynamics theory exemplifies the effectiveness of this blended approach. In more recent research, Yu et al. [78] conducted quantitative assessments of misinformation channels, and Rodicˇ [79] proposed an epidemiological modeling perspective for misinformation. Amoruso et al. [80] and Lotito et al. [81] contributed critical insights into the propagation of misinformation in multiplex networks and the comprehension of information dynamics. From the viewpoint of information governance, Huang [82] analyzed the interplay of private censorship and disinformation, and Gomathy et al. [83] contemplated the balance between free expression and online content regulation. Furthermore, Ishizumi et al. [84] proposed a preventive public health framework, and Torpan et al. [85] performed an international comparative study on misinformation countermeasures in emergencies, emphasizing the necessity of comprehensive approaches to managing the information ecosystem.

Ishii et al. [34] proposed a social simulation focusing on trust and distrust, and Kopp et al. [86] developed an information-theoretic model of cooperation and dissemination in populations exposed to harmful information. In recent theoretical developments, Bazelon [87] analyzed the disinformation dilemma, and Machado [88] discussed new regulatory frameworks for content moderation, highlighting the importance of both technological and social strategies. On the technical side, Kalita et al. [57] suggested a machine learning- based density functional approximation method, hinting at its potential application in network analysis. Sociophysical research by Ishii and Kawahata [31,32] incorporated trust-distrust relationships into opinion dynamics, and Kawahata and Ishii [35] investigated online consensus formation mechanisms.

Ishii and Kawahata [33] further introduced a theory of opinion distribution under mixed trust conditions, emphasizing the significance of social relationships in pinpointing misinformation dissemination routes. Gomathy [83] offered a new perspective on balancing freedom of expression and content regulation, and Conte Complex et al. [69] proposed an integrated approach that combines computational modeling with data analytics for complex social systems. In the realm of theoretical progression, Vasiliev et al. [55] and Mackrodt et al. [56] have laid the groundwork with first principles and DFT-based methods that suggest new possibilities for analyzing social networks. All these findings collectively indicate the need for multifaceted approaches to identifying and managing the spread of harmful information. Notably, the integration of technical solutions and social interventions has been repeatedly stressed. From an empirical standpoint, Tsubokura et al. [53] visualized the dissemination of scientific communication by influencers in disaster scenarios, providing a method to identify critical nodes in the information flow. Bail et al. [52], demonstrating that exposure to adversarial views on social media can intensify political polarization, underscored the negative consequences of information spreading. At the theoretical level, by applying Gonze’s [54] potential-based conjugate gradient algorithm and Zhu et al.’s [18] nonlocal pseudopotential approach, new modeling techniques for information dissemination have been proposed. Focusing on health-related misinformation, Kadakia et al. [76] discussed the role of regulatory agencies, while Marecos et al. [77] considered policy recommendations from the perspective of freedom of expression. Adopting a systemic approach, Hegselmann and Krause’s [28] bounded confidence model laid the groundwork for Kleinberg [63] to analyze social phenomena from algorithmic and network standpoints, offering a more comprehensive interpretive framework. Collectively, these studies suggest that harmful information dissemination is not merely an issue of content spread, but rather a phenomenon intricately entwined with societal, technological, and institutional factors.

Theoretical Developments in the Application of First-Principles Calculations to Social Phenomena in Recent Years

q. Sociophysics and Network Analysis

Kleinberg [63], in ”Algorithms, Networks, and Social Phenomena,” discusses the development of computational models centered on the spread of information and behavior within social networks. In particular, he examines how the underlying network structure influences the dynamics of information transmission and demonstrates that a first-principles approach can be effective in understanding social interactions. r. Advances in Computational Social Science

Conte et al. [64] present four approaches to computational social science methodologies:

• Automated extraction of social information
• Social network analysis
• Theories of social complexity
• Social simulation modeling
These methods serve as frameworks for causally explaining the dynamics of individuals and societies.

s. Progress in Social Computing

Chopra [65], in ”Social Computing: Principles, Platforms, and Applications,” emphasizes the computation of social dependencies among autonomous actors. He proposes a shift from traditional software engineering approaches toward frameworks capable of understanding and computing highlevel social abstractions.

i. Agent-Based Modeling: Hegselmann and Terna [66,67], in ”Simulating Social Phenomena,” underscore the importance of agentbased modeling for simulating social phenomena. They focus on:

• Mechanisms of cooperation
• Patterns of interaction
• Dynamic processes of coalition formation
• Decision-making procedures
• Market dynamics

t. New Perspectives on Applying First-Principles Calculations to Social Phenomena

i. Computational Approaches on a Global Scale: Kleinberg [68], in ”Computational Perspectives on Social Phenomena at Global Scales,” discusses the importance of network structure in social media dynamics and the utility of text data analysis for studying online interactions. He highlights:

a. How network structure influences the dynamics of social media platforms
b. The effectiveness of text data analysis for understanding characteristics of online social interactions

ii. Integrating Computational Social Science with Big Data Analysis: Conte et al. [69] identify the following challenges in the advancement of computational social science:

• While big data analysis provides massive volumes of data, it does not, on its own, yield sufficient insights.
• Integration of social data mining and computational modeling is essential.
• Understanding how macro-level phenomena emerge from micro-level components is crucial.
iii. Physical Modeling of Social Networks: Yuan [89] conceptualizes social networks as physical systems and proposes a Hamiltonian of the form:

These studies suggest that integrating physical approaches [55,56] with social science perspectives [29,30] is integral to understanding social phenomena via first-principles methods. As Ishii et al. [34] have shown, computational techniques are effective for uncovering how macro-level social outcomes emerge from micro-level interactions. Furthermore, the work of Kleinberg [63] and Yuan [89] indicates that this integrative approach will play an important role in future developments in sociophysics.

Risks to Mental Health Posed by Harmful Information and Doomscrolling

The widespread adoption of the internet and social media has dramatically increased both the speed and scope of information dissemination. Nevertheless, concerns have arisen regarding the impact of misinformation and harmful content on mental health [90,91]. In particular, doomscrolling—a compulsive behavior characterized by continuous exposure to negative news—has attracted attention for its psychological consequences. Drawing on the literature, this section discusses the risks that harmful content and doomscrolling pose to individuals and society, including illustrative examples.

• Psychological Impacts of Harmful Information and Examples

Harmful content involves the deliberate transmission of false hoods designed to incite social anxiety and influence recipients’ cognition. Bilal et al. have shown that specific patterns are employed within harmful information to manipulate readers’ emotions, potentially exerting negative effects on mental well-being [90]. For instance, widespread misinformation during the COVID-19 pandemic has led many individuals to refuse vaccination [91]. Similarly, the 2016 U.S. presidential election witnessed the dissemination of false narratives such as “Pizzagate” and conspiracies involving “paid protesters,” causing social unrest [90]. These fabrications evoked fear and anger, reinforcing a psychological state that made recipients more susceptible to accepting other falsehoods.

u. Consequences of Doomscrolling and Examples

Doomscrolling is notably prevalent under crisis conditions and can be viewed as excessive behavior in seeking negative information. This practice leads to psychological repercussions, such as sleep disorders, chronic stress, and feelings of social isolation [92]. For example, repeatedly viewing news about COVID-19 infections and death tolls exacerbated accumulated stress and increased the incidence of anxiety disorders and depressive symptoms [93]. In addition, phenomena have been observed in Korean online news comment sections, where artificially amplified anti-government sentiment reduced ordinary users’ willingness to voice their opinions [91]. Such findings suggest that individuals subjected to an “engineered reality” shaped by misinformation experience heightened psychological burdens.

v. Interaction Between Harmful Information and Doomscrolling

Harmful content and doomscrolling are not independent risk factors; they interact to amplify each other’s detrimental effects. Harmful content induces anxiety and fear, thereby promoting doomscrolling. Simultaneously, excessive consumption of negative information through doomscrolling facilitates the spread of harmful content, creating a vicious cycle [94]. This reciprocal relationship is particularly pronounced during times of social instability, such as elections or pandemics, when emotionally charged harmful information spreads swiftly, intensifying the psychological strain on recipients. The risks these phenomena pose to mental health are severe, impacting not only individual psychological wellbeing but also exerting a deleterious influence on the entire information ecosystem. This discussion draws on the literature to examine the specific repercussions and potential countermeasures.

w. Challenges in Modeling and Identifying Dissemination Pathways of Harmful Information

Over the past three decades, the proliferation of the internet and social media has dramatically expanded the speed and scope of information circulation. Concurrently, harmful and misleading content has increasingly exerted significant social, political, and economic impacts, including distorted election outcomes, heightened social unrest, and threats to public health. Thus, understanding the mechanisms behind harmful information dissemination and devising effective means of control and pathway identification represent urgent challenges

for contemporary society. Although the application of epidemiological models to information dissemination has yielded some achievements, conventional diffusion models fail to fully capture the complexity of online social networks. These networks often exhibit multilayered, interdependent structures, and heterogeneous interactions among users dramatically influence the speed and routes of information flow. Additionally, time-dependent and nonlinear factors— such as algorithmically induced filter bubbles and dynamic correlation across multiple network layers—further complicate pathway identification. This work reviews key challenges in modeling and identifying dissemination routes for harmful information, outlines the limitations of basic diffusion models, and highlights complexities in multiplex networks such as those discussed by Doostmohammadian and Khan [20].

It also considers structural and temporal factors, as well as social and technological barriers, that hinder accurate determination of diffusion pathways. The challenges in modeling and identifying dissemination routes of harmful content are critical to understanding the complexities of information propagation in contemporary society. With social media serving as primary channels of information flow, epidemiological modeling has garnered attention. For instance, Menczer [70] has shown that machine learning techniques can detect astroturfing and social bots, contributing to pattern analysis in information dissemination. Similarly, Ojha et al. [71] demonstrated the effectiveness of epidemiological approaches within online social networks, underscoring the importance of the basic reproduction number R0. Nonetheless, fundamental diffusion models have limitations, particularly in the context of multiplex networks. Xian et al. [72] elucidated the influence of average degree, heterogeneity, and interlayer correlation on diffusion speed in correlated multilayer networks. Rodiˇc [79] employed the SEIZ model, encompassing susceptible (S), exposed (E), infectious (I), and zealot (Z) states, to dissect the complex dynamics of information dissemination. Identifying diffusion pathways is equally challenging. Kopp et al. [86] applied information theory to analyze how a small group of scammers impacts the behavior of a large group of non-scammers, revealing intricate interactions.

Yu et al. [78] emphasized the time-dependent nature of corporate misinformation channels, demonstrating the importance of nonlinear interactions among channels. Social and technological barriers also play a role. Roozenbeek and van der Linden [73] showed that individual media literacy levels and educational backgrounds significantly affect reactions to misinformation. Amoruso et al. [80] highlighted the importance of temporal variability and spatial heterogeneity, while Lotito et al. [81] demonstrated that recommendation systems on social media platforms unpredictably alter diffusion pathways. To address these issues, integrated frameworks combining pathway identification with simulation studies have been proposed. Simpson et al. [74] introduced a Time-Competitive Independent Cascade (TCIC) model that considers differing propagation rates of truth versus falsehood and user response times:

Here, S is the proportion of susceptible individuals, I theproportion of infected (informed) individuals, β the transmissionrate, and γ the recovery rate. Taguchi et al. [75] highlighted the necessity of multisectorcollaboration among researchers, media institutions, technology platforms, and governments, proposing a control system:

where M (t ) represents the amount of misinformation, S (t ) the intensity of social listening, and C(t ) the level of control. Kadakia et al. [76] introduced integrated regulatory frameworks merging institutional and technological approaches. Marecos et al. [77] proposed a model involving regulatory effectiveness R(t ) influenced by media literacy measures M (t ), ethical considerations E (t ) , and legal constraints L(t ):

Huang [99] proposed a content control model from a platform governance perspective:

where C(t ) is content control effectiveness, Pi(t) are platform- specific interventions weighted by wi , and D(t ) represents the impact on democratic values. Ishizumi et al. [84] introduced a preventive framework inspired by public health concepts, proposing a hierarchical prevention model:

where P(t) is the overall preventive effect, and Li (t) and Ei(t) denote the intensity and efficacy of interventions at four prevention levels—primordial, primary, secondary, and tertiary. Gomathy [83] modeled the complexity of information control by examining the interactions among sources, intermediaries, recipients, and governance mechanisms. The control effect E (t ) can be evaluated as:

These studies demonstrate that preventive approaches and sociotechnical integration are indispensable for controlling mis-information [70,71]. Strengthening system resilience, enhancing early detection, and mitigating impacts through a multilayered strategy are emphasized [73,74]. Moreover, the use of GPT-generated data and multi-criteria AHP evaluations can help alleviate data shortages and facilitate model validation and simulation [64,65]. While generative language models can supplement limited datasets, issues of data reliability, ethical concerns, and bias remain [82,83]. Educational implications include bolstering media literacy and critical thinking skills [75,84]. Employing multicriteria AHP evaluations enables designing effective educational programs that consider multiple factors comprehensively. Yet obstacles such as insufficient technological resources, a lack of domain expertise in educational settings, and the standardization of assessment methods persist [59,76,77]. Overall, preventing the spread of harmful information and controlling misinformation requires multifaceted approaches and international cooperation [87,88,85]. Constructing a comprehensive framework that combines technological interventions with social strategies remains a key challenge moving forward.

x. Correspondence Between the Physical Model of TeNPs and the Rigidification of Information

Tellurium-based nanoparticles (TeNPs) form one-dimensional nanowires, causing electrons and phonons

to become localized along a single dimension. This structure induces strong spatial correlations. Possessing robust covalent bonds and strong electronic interactions, the electrons within TeNPs exhibit high electron density and intensive many-body effects. These lead to the formation of energy gaps and electron localization. In analogy to social systems, from the perspective of the rigidification (ossification) of information, the one-dimensional chain structure can represent circumstances in which information becomes entrenched and is impervious to external influences within a closed community or group. **Modeling Stable Communities**: Strong covalent bonding and substantial electronic correlation can be used to model a scenario in which particular information (e.g., harmful content) is firmly retained within a group, making it difficult to correct or modify.

y. Correspondence Between the Physical Model of Graphene

and the Rapid Diffusion of Information Graphene is characterized by its two-dimensional honeycomb lattice structure, composed of carbon atoms arranged in a plane. Within this lattice, electrons can move freely in two dimensions. Because massless Dirac electrons in graphene adhere to the Dirac equation and travel at high speeds, graphene displays exceptional electronic conductivity. Additionally, long-range correlations and the quantum Hall effect highlight the topological properties of electrons. By drawing analogies with social systems, one can hypothesize that the rapid and extensive dissemination of information parallels the two-dimensional structure and high conductivity of graphene, which may serve as a proxy for modeling the swift and widespread propagation of information across a social network. Furthermore, from the perspective of network effects, the long-range mobility of Dirac electrons can model information sharing among distant individuals or represent viral diffusion phenomena.

i. Toward Analyzing Harmful Information Phenomena in Large-Scale Data Using DFT: Considering the rigorous treatment of many-body interactions, density functional theory (DFT) treats these interactions by representing them as functionals of electron density. This feature can be leveraged to model complex, nonlinear human relationships and influence dynamics in social networks. By formulating an energy functional for social networks, it is possible to assume that the system evolves toward minimizing its total energy. This assumption, in turn, allows the analysis of collective opinion formation and the entrenchment of harmful information. Regarding the modeling of difficult-to-resolve phenomena in large-scale datasets, just as DFT can analyze stable states such as electron localization or band gap formation in materials, it can also model the fixation of information and the intractability of harmful content within social networks. From the standpoint of balancing computational efficiency and accuracy, DFT surpasses other first-principles methods in efficiency, making the simulation of large social networks feasible within a realistic timeframe.

ii. Theoretical Background and Considerations for Applying Computational Methods: Within the DFT framework, the Kohn-Sham equations introduce external and exchangecorrelation potentials into the non-interacting Schr¨odinger equation. By applying such concepts to social networks—defining individual state functions and interaction potentials—it becomes possible to analyze changes in individual opinions or behaviors. The exchange-correlation effects between electrons can be interpreted as pressure to conform or imitate others within a social system. By incorporating these considerations into DFT, one can model the processes by which individuals modify their opinions under social influence. By employing linear response theory within DFT, one can investigate how a social system responds to external inputs—i.e., harmful information. This approach can be instrumental in predicting the speed and reach of information dissemination.

Positioning of this Study

Building on the preceding arguments, this study constitutes a novel attempt to apply graphene’s physical model to socio-physics. Specifically, it leverages graphene’s exceptional electronic conductivity and two-dimensional structure to model rapid information dissemination and complex network interactions, thereby analyzing the spread of harmful information from a socio-physical perspective. Prior research has scarcely utilized graphene as a model for social systems, endowing this study with originality and novelty. Moreover, applying first-principles computational techniques from materials science to the social sciences opens up possibilities for analyzing microscopic interactions and largescale datasets—domains previously beyond conventional modeling capabilities. However, the approach demands substantial computational resources. In this work, the discussion will be limited to the use of DFT-based approaches.

z. Overview of First-Principles Calculations and Density

Functional Theory (DFT) First-principles calculations directly derive material properties from fundamental quantum mechanical principles without relying on empirical parameters [18], making them well-suited for predicting the characteristics of unknown substances or systems [55]. DFT computes the ground-state energy of a system based on its electron density [56]. The Kohn-Sham equations map a complex many-body problem onto that of non-interacting electrons, reconciling computational efficiency with precision [57]. Advances in computational technology now enable large-scale DFT computations on systems comprising thousands to tens of thousands of atoms.

aa. Model Construction: Modeling Social Networks

Individual entities (agents) in a social network are modeled, each holding distinct opinions or beliefs [28,69]. Interactions among agents can be defined by an energy function [95]:

Here, Jij is the coupling strength between agents, Bi represents the opinion of agent i , and σ is a parameter reflecting opinion diversity.

i. Applying the Principle of Energy Minimization: The total energy of the system is computed as the sum of pairwise interaction energies [23]:

ii. Energy Minimization and Stable States: Just as physical systems tend toward minimizing energy, we assume that social systems evolve to minimize total energy [24]. This assumption enables explanations for opinion convergence and the entrenchment of harmful information.

ab. Introducing Harmful Information and Modeling Rigidification

Harmful information is introduced as an external potential [70]:

where h represents the influence of harmful information and Fi is an indicator showing whether agent i is exposed to it. Redefining total energy:

ac. Modeling the Rigidification Process

During the process of energy minimization, if the influence of harmful information is strong, agents’ opinions will align with that information, stabilizing this pattern [71].

ad. Conducting Simulations

To set up the simulation environment and hypothesize a network, a hybrid network combining the one-dimensional chain of TeNPs with the two-dimensional lattice of grapheneis constructed [72]. −Jij : coupling strength between agents. It is set to be strong in the TeNP model and weak in the graphene model [79]. −σ :

a parameter indicating opinion diversity [86]. −h : the influence of harmful information [78]. Each agent’s initial opinion Bi(0) is assigned randomly [73].

ae. Simulation Procedure

• Introducing Harmful Information: Inject harmful information into specific agents or groups [80].

• Energy Calculation: Compute the total system energy total Etotal [81].

• Energy Minimization: Use methods such as Monte Carlo simulations to seek states that minimize energy [33].

• Opinion Update: Update each agent’s opinion Bi based on the results of energy minimization [34].

• Convergence Check: Terminate the simulation when changes in energy fall below a certain threshold [74].

To prevent node name conflicts, a prefix (’G−’ for graphene and ’T −’ for TeNPs) was attached to each node name. Moreover, to facilitate information exchange between the graphene and TeNP segments, edges were added between the first five nodes of the graphene section (G-0 to G-4) and the first five nodes of the TeNPs section (T-0 to T-4). This integration enabled the free transmission of information across both networks.

ii. Network Visualization: Figure 2 illustrates the hybrid network Gsocial. The node positions were calculated using spring_layout, providing a visual representation of the network’s overall structure.

Computational Results: Simulating Harmful Information Dissemination Across Different Network Sizes

This section provides a detailed account of simulations of harmful information dissemination while varying network size. The simulations are performed on a hybrid network that integrates the honeycomb lattice structure of graphene with the one-dimensional chain structure of TeNPs.

af. Construction of the Hybrid Network

In this study, a hybrid network was assembled by integrating the honeycomb lattice structure of graphene with the one-dimensional chain structure of tellurium-based nanoparticles (TeNPs), enabling simulations of the spread of harmful information.

i. Network Generation: First, a network Ggraphene emulating the honeycomb lattice of graphene was generated. Using the NetworkX library’s hexagonal_lattice_graph function, a two-dimensional hexagonal lattice with 5 rows and 5 columns was created. Next, a network GTeNPs , representing the one-dimensional chain structure of TeNPs, was generated with the path_graph function to produce a path graph of 25 nodes. These two networks were then combined to form the hybrid social network Gsocial :

Figure 2

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ag. Mathematical Representation of the Network

ah. Initial Conditions for the Simulation

Before commencing the simulation, initial opinion values are assigned to each node. All nodes begin with an initial opinion value of 0, except those designated as sources of harmful information, which are assigned a value of 1. This initialization allows observation of how harmful content propagates throughout the network.

i. Simulation Parameters: The simulation is run under the following parameters:

• Network Size:

a. Small-scale network: (Nrow, Ncol, LTeNPs)= (5,5,25)

b. Medium-scale network: (10, 10, 50)

c. Large-scale network: (15, 15, 75)

• Harmful Information Source: Node ’T-0’

• Initial Opinion Values: 0 assigned to all nodes

• Diffusion Coefficients and Fixation Parameters:

• Time Steps: T = 20

ii. Opinion Dynamics Model: The opinion value oi(t) of each node i at time t is updated as follows:

After updating, the opinion value is clipped to the range [−1, 1]:

iii. Visualization of Simulation Results: For detailed visualization, each simulation’s results are presented in figures containing 10 subplots. The node layout is calculated using spring_layout, and node colors represent opinion values (from −1 to 1 mapped onto a blue-to-red colormap).

ai. Hierarchical Structure of Interactions

aj. Results and Discussion

A detailed analysis of the simulation results across multiple graphs at each timestep was conducted to examine the ossification of harmful information within the graphene-TeNPs hybrid structure.

i. Quantitative Assessment of Temporal Evolution Patterns: Distinct differences were observed between the initial (Step 0-9) and later stages (Step 10-19) of time evolution, as shown in Table 1. These temporal patterns closely correlate with structural dependencies. Table 2 shows the properties of the graphene and TeNPs sections. Table 3 shows how chain length in the TeNPs segment influences information intensity. Notably, distance-dependent attenuation was observed, as shown in Table 4. Based on these analyses, insights were derived for system optimization, summarized in Tables 5-20.

Table 1: Temporal Evolution Characteristics by Network Size.

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Table 2: Properties By Structural Region.

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Table 3: Information Transmission Characteristics by Tenps Chain Length.

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Table 4: Distance-Dependent Information Intensity Changes from the Junction.

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Table 5: System Optimization Parameters.

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Table 6: Detailed Impacts of Digital Challenges on Mental Health [14- 20].

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Table 7: Interconnections Among Causes of Harmful Information.

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Table 8: Comparison of Material Characteristics.

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Table 9: Model Constraints and Limitations.

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Table 10: Notable Phenomena in Basic Structures.

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Table 11: Propagation Delay Effects Due to Tenps Structure.

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Table 12: Evaluation of Directional Control Characteristics.

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Table 13: Temporal Evolution of Diffusion Patterns.

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Table 14: Infection Characteristics by Structure.

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Table 15: Assessment Of Boundary Effects.

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Table 16: Time-Series Behavior Under Threshold Set 1.

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Table 17: Opinion Value Increase Rate in the Tenps Chain.

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Table 18: Diffusion Properties in the Graphene Structure.

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Table 19: Propagation Efficiency at the Junction.

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Table 20: Final Diffusion Rate by Threshold.

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ak. Information Control Analysis in the Graphene-Tenps Hybrid Structure

This analysis highlights key factors influencing the ossification system within the graphene-TeNPs hybrid structure:

i. Combining Structures with Different Diffusion Characteristics

• Graphene segment: Rapid diffusion (1.5×/step)
• TeNPs segment: Linear propagation (0.2×/step)

ii. Effects of Network Size

• Doubling network size increases total diffusion time by
• approximately 1.8×
• Initial diffusion speed decreases by approximately 0.7×
• Terminal information intensity decreases by about 65%

iii. Characteristics of the Ossification Mechanism

• 90% information intensity attenuation in the TeNPs region Transmission efficiency at junctions reduced to 30%
• Efficiency decline of about 45% as network size increases

Particularly noteworthy is the finding that the most effective rigidification is achieved in large-scale networks (15×15). This result appears to arise from the combined effects of two factors: the suppression of initial diffusion due to the ample surface area of the graphene section, and the effective attenuation of information intensity resulting from the extended TeNPs segment length. Furthermore, it has been revealed that controlling the transmission efficiency at the junction plays a decisive role in determining the overall system performance. Specifically, maintaining the transmission efficiency around 30% at the junction consistently yields optimal rigidification outcomes. These insights offer tangible guidelines for designing systems to ossify harmful information dissemination. In particular, selecting an appropriate combination of network size and TeNPs length, as well as optimizing junction properties, proves indispensable for effective implementation. As the network expands, the speed of information diffusion declines. This observation can be attributed to the increased number of nodes and path lengths within the network, which, in turn, diffuse the influence exerted on individual nodes. Moreover, due to the high diffusion coefficient in the graphene portion, information propagation in that region is enhanced, whereas in the TeNPs segment, where the fixation parameter is low, information spread tends to be inhibited.

Simulation of Harmful Information Dissemination Using the Sir Model

This section describes a simulation method employing the SIR model to analyze the spread of harmful content. The simulation is implemented in Python and conducted on a hybrid network combining the honeycomb lattice structure of graphene and the one-dimensional chain arrangement of TeNPs.

a. Model Overview: The SIR model is a classical mathematical framework for modeling the spread of infectious diseases, comprising agents in one of three states [96]:

• Susceptible (S): Agents who may become infected but are not yet infected.

• Infected (I): Agents who have contracted the infection and can transmit it to others.

• Recovered (R): Agents who have recovered from the infection and cannot be reinfected.

In the context of harmful information dissemination, these states can be interpreted as follows:

• S: Agents who have not yet encountered the harmful information.

• I: Agents who have received the harmful content and are capable of spreading it further.

• R: Agents who have lost interest in the harmful material and do not propagate it.

b. Simulation Setup: The following parameters are employed in the simulation:

• Infection Rate β: The probability that an infected agent transmits harmful information to a susceptible one.

• Recovery Rate γ: The probability that an infected agent transitions to a recovered state.

The parameter values are set as:

The network size is fixed, with the graphene portion represented as a 5×5 honeycomb lattice and the TeNPs portion as a one-dimensional chain of 25 nodes.

c. Simulation Procedure: The simulation is executed as follows:

Network Construction: Generate the hybrid network modeling the graphene and TeNPs structures.

Initialization: Set all agents to the susceptible state (S), except for the designated harmful information source

• Nodes, which are set to infected (I).

State Update: At each time step, repeat the following processes:

i. Infected agents (I) recover with probability γ and become recovered (R).

ii. Infected agents (I) transmit the harmful information to adjacent susceptible agents (S) with probability β.

Record Results: Document the state of each agent at every time step.

d. Mathematical Model: For sufficiently large populations, the SIR model can be represented by the following differential equations:

where S, I, and R denote the fractions of agents in each state. In this simulation, transitions are tracked on a per-agent basis through probabilistic updates.

Results and Discussion

Figure 3 depicts the network’s state at each time step. Node colors indicate Susceptible (blue), Infected (red), and Recovered (green) agents, allowing real-time visual monitoring of changes over time. Figure 4 shows the variation in the number of infected agents with time. By altering the combinations of infection rate β and recovery rate γ, one can compare the differing infection dynamics.

Figure 3

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Figure 4

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Analysis of Structural Characteristics and Patterns of Harmful Information Dissemination

Using the time-series images in Figure 3, we analyze structural features and dissemination patterns in detail.

al. Quantitative Evaluation of Control Mechanisms

am. Quantitative Characteristics of the Graphene Structure and Related Insights: The simulation results yield the following conclusions:

• When the infection rate β is high, the number of infected agents rises rapidly, facilitating extensive dissemination of harmful information across the entire network.

• As the recovery rate γ increases, the peak number of infected individuals diminishes, and the diffusion process tends to converge more promptly.

• Due to the hybrid network architecture, the pattern of information propagation becomes more intricate, resulting in phenomena where information becomes entrenched in specific areas.

By employing the SIR model, it was possible to analyze the dynamics of both the spread and eventual convergence of harmful information. Adjusting the infection and recovery parameters suggests that it may be feasible to control the speed and extent of information dissemination.

i. Propagation Delay Effects: The TeNPs structure contributes the following effects:

• Approximately a five-step delay in information propagation:

Early phase (0-3 steps): Provides temporal leeway for verifying information.

Intermediate phase (3-5 steps): Facilitates gradual propagation control.

• Gradual regulation of the number of infected nodes:

Initial stage: 1-2 nodes

Maximum spread: 3-4 nodes

Convergence: 2-3 nodes

ii. Directional Control Mechanisms: Structural characteristics enable the following forms of regulation:

• Control at junctions:

– Maintaining an infection rate of about 30% at the graphene- TeNPs junction.

– Realizing a filtering function for information flow.

• Propagation speed regulation:

– Within the TeNPs structure: About one-third the speed compared to the graphene section.

– At terminal regions: Below 10% infection probability.

iii. Role of the Graphene Structure: As the fundamental framework for information diffusion:

Diffusion characteristics:
– Isotropic information distribution.
– Predictable propagation patterns.
• Control functions:

– Natural propagation limits induced by boundary effects.
– Regular temporal evolution of cluster formation.
– Manageability of cluster merging processes.

From this analysis, one of the most significant insights in this preliminary study is that the TeNPs structure functions as a “buffer” for information diffusion. Due to this feature:

i. There is sufficient time for verifying information.
ii. Stepwise control of propagation speed is achievable.
iii. Structural filtering of information can be implemented.

These findings highlight the high potential effectiveness of adopting a structural approach to counter harmful information. In particular, by combining the properties of the graphene framework with the attributes of the TeNPs configuration, it becomes possible to envision more effective control systems.

Simulation 0f Harmful Information Dissemination Using a Threshold Model

Lastly, this study details simulations of harmful information propagation employing a threshold model. These simulations were performed on a hybrid network derived from the honeycomb lattice structure of graphene and the one-dimensional chain arrangement of TeNPs.

an. Opinion Dynamics with a Thresh oi(t) ∈ old Model

Each node maintains an opinion value {0,1} , which is updated over time. According to the threshold model, a node’s opinion changes if the proportion of neighboring nodes expressing agreement surpasses its threshold. For each node i , a threshold value θi ∈ [0,1] is assigned. In this simulation, the same threshold θ is used for all nodes.

i. Opinion Update Rules: At time step t, the opinion of node i , oi (t), is updated as follows:

Here, N (i) is the set of neighbors of node i , and | N (i) | is its cardinality. In other words, if the proportion of neighboring nodes with opinion “1” exceeds θi , node i adopts opinion “1.”

ao. Simulation Parameters

The simulation was executed under the following conditions:

Network Size: ( Nrow, Ncol, LTeNPs ) = (5, 5, 25) • Harmful Information Source: Node ’T − 0’ • Initial Opinions: oi(0) = 0 for all nodes, except for the source node oT-0(0)=1 • Threshold Values: θ = {0.3,0.5,0.7} • Number of Time Steps: T = 20

ap. Results and Considerations

Figure 1 shows the simulation results for each threshold setting, visualizing the distribution of opinions at each time step. Nodes displayed in red hold opinion “1” (agreement), while nodes in blue hold opinion “0” (disagreement). Figure 5 illustrates the temporal changes in the average opinion value.

Figure 5

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aq. Structural Dependence in Temporal Evolution

• The average opinion stabilizes around 0.01 throughout the entire period.
• Propagation suppression in the TeNPs one-dimensional chain.
• Extremely limited diffusion within the graphene structure.
• Minimal interaction between the two structural components.
• The average opinion remains below 0.005.
• Near-complete suppression of diffusion.
• Structural characteristics are negated by threshold effects.
• Almost complete obstruction of propagation in both structures.

ar. Structure-Specific Quantitative Analysis: Propagation Efficiency within the TeNPs Chain

as. Quantitative Evaluation of Inter-Structural Response Characteristics

These findings from the model underscore that the precise control of structural characteristics and threshold effects is pivotal for achieving ossification of harmful information dissemination within the graphene-TeNPs composite framework. In particular, operational adjustments around the threshold of0.5 suggest the potential for effective propagation management while capitalizing on structural attributes.

Conclusion

This study proposed a preliminary attempt to apply first-principles calculations—specifically, Density Functional Theory (DFT)— and physical models of tellurium-based nanoparticles (TeNPs) and graphene to sociophysics. By exploring the dynamics of harmful information dissemination and ossification in large-scale datasets, the simulation results demonstrated that it is indeed possible to reproduce both the fixation of information and its rapid spread. Moving forward, it will be necessary to verify the universality and validity of these hypotheses through empirical data and comparisons with other material-based models. The investigations highlighted the necessity of a preventive approach and a sociotechnical integration in mitigating misinformation. In particular, multilayered strategies that enhance system resilience, facilitate early detection, and moderate impacts are crucial. Previous research organized the multifaceted challenges in modeling and identifying harmful information diffusion paths. While epidemiological models and multiplex network analyses have made progress, the complexity and variability of online social platforms demand consideration of factors such as cross-border information movement, the unpredictability of user behavior, and algorithmic interventions. Overcoming these challenges requires integrated strategies and frameworks that incorporate legal and ethical guidelines, as well as comprehensive management of the information ecosystem. Systemic fortification, educational initiatives, early detection measures, and impact mitigation should be implemented simultaneously, with collaboration among technology platforms, media organizations, governments, and educational institutions. Such efforts, by preserving information trustworthiness and social integrity, will help build a sustainable digital information environment (Figures 6-21).

Figure 6

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Figure 7

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Figure 8

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Figure 9

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Figure 10

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Figure 11

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Figure 13

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Figure 14

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Figure 15

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Figure 18

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Figure 19

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Figure 20

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Figure 21

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at. Simulation Results and Analysis: A Preliminary Study of Ossification Patterns in Harmful Information

In terms of computational efficiency, the DFT-based model enables simulations of large-scale networks within realistic timeframes [66]. Identifying ossification patterns and diffusion routes of harmful information fosters the potential to detect abnormal propagation [63]. In the TeNPs segment, the data suggest that harmful information becomes firmly embedded, making agents’ opinions resistant to external influence [65]. Conversely, the graphene-model segment displays rapid, extensive spread of harmful content affecting numerous agents, as confirmed from the network structure [64]. The hybrid network reveals both fixation and swift dissemination, reproducing the duality of harmful information [69]. Parameter dependence analyses indicate that larger influence parameters (h) intensify information fixation and increase agents’ tendency to conform to harmful content [68]. Moreover, a smaller opinion diversity parameter (σ) suggests a greater difficulty in achieving information fixation due to heightened opinion differences.

i. Potential Applications of the Graphene Physical Model to Socioeconomic Phenomena: Graphene is a unique material composed of carbon atoms arranged in a two-dimensional honeycomb lattice, where electrons behave as massless Dirac fermions governed by the Dirac equation. Its salient characteristics include extraordinarily high electron mobility, exceptionalelectrical conductivity even at room temperature, and remarkable mechanical strength despite atomic-scale thickness.Observations of the quantum Hall effect underscore the importance of topological properties in determining its systemwide behavior. Although direct applications of the graphene physical model to understand social or economic phenomena are currently limited, numerous studies have employed physics-based concepts and models in the social sciences and economics.

These include:

Network theory: Using lattice models or network frameworks from physics to examine the structure and dynamics of social and economic networks.
Phase transitions and critical phenomena: Modeling abrupt changes in social systems (e.g., economic crises or viral outbreaks) as phase transitions in physical systems.
Small-world phenomena: Employing graph theory to analyze the efficiency of human interactions and information diffusion.

Graphene’s distinctive properties may provide fresh perspectives in modeling social systems. Its high electron mobility can serve as an analogue for the rapid and extensive spread of information or influence across social networks. The honeycomb lattice structure could represent complex network patterns, potentially modeling interpersonal relationships or organizational structures. The quantum Hall effect’s topological characteristics imply that network-level structure can override individual node properties, echoing social systems where collective dynamics surpass individual elements. IntegratingIntegrating machine learning for improved anomaly detection and exploring other social phenomena also remains promising.

Perspectives on Care in the Context of Harmful Information and Doomscrolling

Harmful information and doomscrolling impose direct psychological stress on recipients, undermining societal trust and individual judgment. As demonstrated by this study, while both the fixation and rapid diffusion of information are observed in the network, psychological care at both individual and societal levels becomes critical [91]. For example, introducing psychotherapeutic interventions or mindfulness programs can mitigate emotional reactions induced by harmful content. To alleviate doomscrolling habits, strategies like digital detox and time-management tools are recommended [93]. The characteristics gleaned from the graphene model’s rapid propagation and the TeNPs model’s fixation properties can guide strategies for disseminating reliable information. Enhancing algorithmic detection of falsehoods on social media and prioritizing credible sources could reduce the influence of harmful information [94]. Strengthening media literacy through educational institutions and public policies is indispensable for preventing the spread of misinformation. Developing and disseminating educational programs on evaluating sources and identifying falsehoods is particularly crucial [97-99]. Awareness campaigns highlighting the risks of doomscrolling and promoting healthy information consumption can further help individuals and communities understand the ramifications of harmful content dissemination and adopt effective coping measures.

Acknowledgments

This study is supported by the Japan Society for the Promotion of Science (JSPS) ”KAKEN” Grant-in-Aid for Scientific Research project “A Quantitative-Qualitative Integrative Study of National Populism Mediated by Quantitative Text Analysis,” Project/Area Number 24K0031(2024-2026). This manuscript is a revised version of ”Introducing First-Principles Calculations: New Approach to Group Dynamics and Bridging Social Phenomena in TeNP-Chain Based Social Dynamics Simulations,” originally submitted to arxiv on March 6, 2024. We have incorporated both positive and negative feedback received since its submission. We extend our sincere gratitude to the many colleagues in physics who provided guidance and insights, as well as to all stakeholders whose contributions facilitated the progress of this research.

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