Mechanical modeling of friction phenomena in social systems based on friction force

In physics, friction is a phenomenon where two or more objects move in the tangential direction of the contact surface or have a relative movement tendency; the force between the contact surfaces that hinders relative movement is the friction force. Humans have long recognized both the useful and detrimental aspects of friction. Friction is ubiquitous not only in natural sciences but also in social sciences, where it appears as political differences, cultural boycotts, and other conflicts. With accelerating globalization, industrialization, and urbanization, modern societies experience extensive changes accompanied by frictions stemming from benefit distribution, cultural exchanges and collisions, and technological innovation, which may induce instability and turbulence. Recent research has examined social frictions across domains such as consumption choices, technological use, data sharing, and livelihood conflicts. However, due to the lack of systematic global thinking, the types and structures of social friction phenomena remain unclear. Drawing on social physics and management mechanics, this study aims to: define social friction and its characteristics; construct a social friction force model grounded in friction force and classical mechanics; and analyze the emergence and evolution of social friction phenomena from a mechanics perspective.

Related works on social physics: Social physics applies quantitative, mathematically grounded methods to study complex social phenomena and collective human behavior. Prior research has used physical concepts (e.g., kinetic and potential energy, statistical physics, gravity analogies) to model financial volatility, group conflicts, ethical behavior, and fair distribution, demonstrating the value of physics-based methods for social problems and governance. Related works on social friction: The term social friction has been used to describe antagonism and resistance across social contexts, including interpersonal problems, state repression, consumption choices influenced by interpersonal exchanges, and arguments with close relations. Frictions permeate individuals, institutions, and environments, often slowing development in growth, economy, and innovation. New technologies introduce novel frictions (e.g., technological, data, and information frictions). Frictions can sometimes be beneficial (e.g., improving decision quality or driving innovation) but excessive friction can hinder development, impose costs, and trigger mass incidents or inefficiencies. Related works on social mechanics modeling: Building on the notion of social force (e.g., social force model for pedestrian dynamics), scholars have modeled crowd movement, opinion dynamics, and other social processes using mechanics principles. Various refinements address stability, computation, and agent initiative. These efforts establish a theoretical foundation for applying friction force and classical mechanics analogies to social systems.

The study employed grounded theory to structure and theorize social friction phenomena and to inform a mechanics-based modeling approach. Data sources and selection: Literature was retrieved from Web of Science (SCI and SSCI) and China National Knowledge Infrastructure (core journals), using friction-related topic terms across social science, philosophy, humanities, economics, and management through 2023. The identification process yielded 3,627 Chinese and 1,002 English items initially; after screening titles/keywords/abstracts, 1,468 Chinese and 552 English remained; after full-text screening, 106 Chinese and 120 English articles were retained, totaling 226 items for qualitative analysis. Grounded theory procedures: Core sentences and high-frequency terms related to social friction were extracted and coded through a three-level grounded coding process. Three researchers independently coded and cross-checked for reliability. Ten social science experts were interviewed to validate and supplement coding results. The final coding outcome comprised 48 initial codes, 11 main categories, and 3 core categories. This process clarified structural characteristics and two-dimensional explicit vs. implicit social friction types. Model construction via mechanics analogies: Building on comparability between physical and social systems and social force model extensions, the study conceptualized social friction force as measuring the intensity of contradictions and conflicts among social elements. The general form is: f_s = α·F + ε, where α is a social friction coefficient determined by intrinsic properties of the social system in a period, F is resultant interaction, and ε is a random error term. Inter-element force is decomposed as F_ij = β·F_ps + γ·F_ph, where β and γ are constants set per model context; F_ps represents mental force and F_ph physical force. The work done by social friction force over time is defined as its social contribution: W = ∫ from 0 to t of f dt. The model adapts static vs. dynamic friction notions by introducing a threshold f_max (maximum static friction force an orderly organization can bear). When f_s < f_max, friction behaves like static friction and is associated primarily with implicit frictions; when f_s > f_max, it behaves like dynamic friction associated with explicit frictions. The sign of W depends on whether friction aligns with or opposes the direction of orderly social development.

- The study distinguishes a two-dimensional structure of social friction phenomena: Implicit frictions (internal roots): cultural, cognitive, interpersonal, technological, and information frictions. Explicit frictions (external manifestations): behavioral, migration, economic, and institutional frictions. - Interactive and evolutionary relationships exist between implicit and explicit frictions: implicit frictions are root causes; explicit frictions are manifestations of accumulated implicit frictions; both generate friction costs (economic and non-economic). - Grounded analysis outcomes: 226 studies analyzed (106 Chinese, 120 English); coding produced 48 initial codes, 11 main categories, and 3 core categories; insights were validated via interviews with 10 experts and cross-checked by three coders. - Mechanics-based model of social friction force: f_s = α·F + ε with inter-element forces F_ij = β·F_ps + γ·F_ph. The cumulative work (contribution) over time is W = ∫ f dt, with W > 0 indicating positive contribution (driving development) and W < 0 indicating negative contribution (hindering development). A critical threshold f_max distinguishes static-like (implicit) from dynamic-like (explicit) regimes. - Regime insights: When f_s < f_max (static-like), implicit frictions can be synergistic and positively contribute to development (e.g., cultural and cognitive differences stimulating innovation; W > 0). When f_s > f_max (dynamic-like), explicit frictions emerge (institutional, economic, behavioral, migration), typically imposing friction costs and potentially yielding W < 0 if opposing orderly development. Under cooperative, positive-sum behaviors, even dynamic regimes can yield W > 0 through synergy (1+1>2). - Empirical illustrations from literature: Trade frictions can damage welfare and GDP for participants and partners; migration frictions hinder population flows and productivity; however, certain trade frictions may induce optimization of employment structures and spur high-quality innovation; environmental benefits (reduced emissions) may occur under some friction scenarios. - Policy and management implications: Promote cooperative strategies to harness beneficial friction and increase positive contributions; implement governance and supervision to reduce conflictual behavior; expand system capacity (increase f_max) to enhance societal stability.

The research question centers on defining, structuring, and modeling social friction phenomena using mechanics principles and assessing how such frictions contribute to or hinder social development. By articulating an explicit-implicit taxonomy and mapping it to static-like versus dynamic-like friction regimes, the study provides a coherent framework linking micro-level interactions (mental and physical forces) to macro-level outcomes (positive or negative contributions). The work formalizes when and how frictions can be constructive (W > 0) versus destructive (W < 0) and identifies a threshold (f_max) that delineates stable, synergistic operation from destabilizing conflict. This addresses the need for a systematic, physics-informed approach to classify and interpret diverse frictions across domains (economic, institutional, technological, cultural, cognitive). The findings emphasize that friction is not inherently detrimental: in alignment with development direction and below critical thresholds, implicit frictions can enhance innovation and governance reform, while explicit frictions often require policy interventions to avoid negative-sum dynamics. The framework’s relevance spans social governance, organizational management, and policy design, guiding the selection of cooperative strategies, conflict mitigation, and capacity-building measures to leverage friction productively.

The study clarifies the two-dimensional explicit-implicit structure of social friction (implicit: interpersonal, cognitive, cultural, information, technological; explicit: behavioral, migration, economic, institutional). It constructs a social friction force model extending social force concepts, defining f_s = α·F + ε with inter-element forces combining mental and physical components and defining the cumulative work W as social contribution. The model explains the emergence and evolution of frictions: f_s below f_max aligns with implicit, static-like frictions that can positively contribute to development; f_s above f_max shifts to explicit, dynamic-like frictions that often impose costs but can yield positive outcomes under cooperative strategies. This mechanics-based perspective enables modeling and potential quantification of social friction, offering a new theoretical lens for interdisciplinary research in social physics and management science. Future research should test and refine the model with additional parameters, quantitative measurement, and real data, and examine both costs and benefits of frictions to inform prevention, management of harmful frictions, and maximization of beneficial ones.

- Parameterization is limited: the current model considers a restricted set of parameters and rules; additional mechanical models and reconstructed variables are needed to enhance realism. - Lack of quantitative validation: the study does not conduct quantitative analyses or use real-world data; measuring and calculating social friction force remains a key future direction. - Focus on costs over benefits: the analysis emphasizes friction costs, whereas frictions can also yield benefits for development and engagement; future work should assess both sides and management strategies to minimize harm and maximize gains. - Scope: the study serves as an introduction to social friction phenomena and the social friction force model, intended to stimulate further inquiry rather than provide exhaustive empirical testing.