Statistical physics of social dynamics
2007/10/17 by Claudio Castellano, Santo Fortunato, Vittorio Loreto · 3 voices · 326 citations
Physics and Astronomy · Social Sciences · #Complex Network Analysis Techniques #Evolutionary Game Theory and Cooperation #Opinion Dynamics and Social Influence #cond-mat.stat-mech #physics.comp-ph #physics.soc-ph
paper · pdf · doi:10.1103/revmodphys.81.591
published as Reviews of Modern Physics 81, 591-646 (2009) · 58 pages, 22 figures. Final version published in Reviews of Modern Physics
arxiv created 2009/05/11 · openalex publication_date 2009/05/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.
Citations
Cited by
- Agent Based Models and Opinion Dynamics as Markov Chains
- Efficient Promotion Strategies in Hierarchical Organizations
- Disinformation by Design: The Use of Evidence Collages and Platform Filtering in a Media Manipulation Campaign
- Collective attention under digital exposure: A dynamical systems approach
- Does Socialization Emerge in AI Agent Society? A Case Study of Moltbook
- Reducibility of higher-order to pairwise interactions: Social impact models on hypergraphs
- Emergence of Chimeras States in One-dimensional Ising model with Long-Range Diffusion
- Exploring Emergent Topological Properties in Socio-Economic Networks through Learning Heterogeneity
- Group size effects and collective misalignment in LLM multi-agent systems
- PEDRA: Evaluating the Realism of Pedestrian Dynamics in Video Generation
- When Your AI Agent Succumbs to Peer-Pressure: Studying Opinion-Change Dynamics of LLMs
- Steady-state phase transition in one-dimensional quantum contact process
- Generalizing Condorcet's Jury Theorem to Social Networks
- Three predictions on July 2012 Federal Elections in Mexico based on past regularities
- Data-Driven Modeling of U.S. Ideological Dynamics
- Patterns of Emotional Blogging and Emergence of Communities: Agent-Based Model on Bipartite Networks
- Modelling Territorial Dynamics through Statistical Mechanics: An Application to Resident Foreign Population
- The effect of social balance on social fragmentation
- Geometric vulnerability of democratic institutions against lobbying: a sociophysics approach
- Restoring detailed balance in non-Hermitian Markov processes
- Consensus as cooling: a granular gas model for continuous opinions on structured networks
- Dynamics of feedback Ising model
- Numerical methods for quasi-stationary distributions
- Empirical validation of the polarization transition in a double-random field model of elections
- Symmetry breaking in collective decision-making through higher-order interactions
- Heterophilious dynamics enhances consensus
- SkyHash: a Hash Opinion Dynamics Model
- Network entropy as a key to the past: A quantitative approach to complex social networks
- Replication and Information Extraction in a Minimal Agent-Environment Model
- Universal Statistics of Competition in Democratic Elections
- Modeling confirmation bias and polarization
- A scaling theory of armed conflict avalanches
- Spatial evidence that language change is not neutral
- Mean-field theory of the general-spin Ising model
- Ising dynamics on multilayer networks with heterogeneous layers
- Controversy-seeking fuels rumor-telling activity in polarized opinion networks
- A semantic embedding space based on large language models for modelling human beliefs
- Instability of social network dynamics with stubborn links
- The grammar of the Ising model: a new complexity hierarchy
- A noisy opinion formation model with two opposing mass media
- Induced Percolation on Networked Systems
- Frustration, glassy behavior and dynamical annealing in societies of Neural Networks
- The temporal dynamics of group interactions in higher-order social networks
- Group interactions modulate critical mass dynamics in social convention
- Graph-Coupled HMMs for Modeling the Spread of Infection
- An accurate mean-field equation for voter model dynamics on scale-free networks
- From cognitive coherence to political polarization: A data‐driven agent‐based model of belief change
- Knowledge transfer in a tourism destination: the effects of a network structure
- Optimal Feedback Control in Social Networks in a McKean-Vlasov-Friedkin-Johnsen System
- Neuromorphic Intelligence
- Control to flocking of the kinetic Cucker-Smale model
- Schrödinger-invariance in the voter model
- Vortex triplets, symmetry breaking, and emergent nonequilibrium plastic crystals in an active-spinner fluid
- Interacting many-body non-Hermitian systems as Markov chains
- Opinion polarization and its connected disagreement: Modeling and modulation
- The Naming Game on the complete graph
- A social force evacuation model with the leadership effect
- Dynamical Systems on Networks: A Tutorial
- Stewardship of global collective behavior
- Explosive adoption of corrupt behaviors in social systems with higher-order interactions
- Finite-time consensus in a compromise process
- Universality and Invariance in Hegselmann-Krause Opinion Dynamics: Proof of Three Conjectures
- Diffusion-driven pattern formation in an opinion dynamical network model
- Modeling Dynamical Influence in Human Interaction Patterns
- Models of Opinion Dynamics with Random Parametrisation
- The Mathematical Theory of Behavioural Swarms: Towards Modelling the Collective Dynamics of Living Systems
- Selection in Scientific Networks
- Robustness and efficiency of leaderless probabilistic consensus protocols within Byzantine infrastructures
- Temperature-Noise Interplay in a Coupled Model of Opinion Dynamics
- The closed loop between opinion formation and personalised recommendations
- The structure and dynamics of multilayer networks
- Time-delayed opinion dynamics with leader-follower interactions: consensus, stability, and mean-field limits
- Cognition in Superposition: Quantum Models in AI, Finance, Defence, Gaming and Collective Behaviour
- Replicator Dynamics of Co-Evolving Networks
- Wealth Inequality in Agent-Based Economies: The Dominant Role of Social Protection over Growth
- Higher-order interactions shape collective human behaviour
- Order-disorder-order transitions and winning margins' scaling in kinetic exchange opinion model
- When group level is different from the population level: an adaptive network with the Deffuant model
- Three quantitative predictions based on past regularities about voter turnout at the French 2009 European election
- Collective contributions to polarization in political voting
- The role of zealots in the spread of linguistic traits
- Binary Decision Process in Pre-Evacuation Behavior
- Social insect colony as a biological regulatory system: Information flow in dominance networks
- A Statistical Physics perspective on fairness in shared expenses: The bar bill analogy
- An Optimization-Based Generative Model of Power Laws Using a New Information Theory Based Metric
- Modeling controversies in the press: the case of the abnormal bees' death
- Robust Fragmentation Modeling of Hegselmann-Krause-Type Dynamics
- Convergence of type-symmetric and cut-balanced consensus seeking systems (extended version)
- Opinion formation in Wikipedia Ising networks
- Beyond Classical Models: Statistical Physics Tools for the Analysis of Time Series in Modern Air Transport
- Continuous-Time User Modeling in the Presence of Badges: A Probabilistic Approach
- Computational Human Dynamics
- Phonetic change in an Antarctic winter
- BOUNDED CONFIDENCE MODEL ON GROWING POPULATIONS
- Mathematical formalism of physics of systems with motivation
- Controlling Communication Field of Complex Networks by Transformation Method
- PSPACE-Completeness of Majority Automata Networks
- Nonmonotonic consensus transitions in bounded-confidence dynamics on unbiased networks
- Exact epidemic models from a tensor product formulation
- Continuous-Time Consensus under Non-Instantaneous Reciprocity
- Collective motion
- Coevolution spreading in complex networks
- An introduction to stochastic self-assembly: theory, simulation and experimental applications
- Kinetic theory of decentralized learning for smart active matter
- Higher order interactions destroy phase transitions in Deffuant opinion dynamics model
- Social polarization promoted by sparse higher-order interactions
- Dynamics of systems with varying number of particles: from Liouville equations to general master equations for open systems
- Interdependent network reciprocity in evolutionary games
- Does strong heterogeneity promote cooperation by group interactions?
- Coevolutionary games - a mini review
- Evolution of the most common English words and phrases over the centuries
- Evolutionary dynamics of group interactions on structured populations: A review
- Statistical physics of crime: A review
- The sensitivity of the Deffuant model to measurement error
- Saving Human Lives: What Complexity Science and Information Systems can Contribute
- Self-organization of punishment in structured populations
- Noise Leads to Quasi-Consensus of Hegselmann-Krause Opinion Dynamics
- From Kinetic Theory to AI: a Rediscovery of High-Dimensional Divergences and Their Properties
- Multicolored Dynamos on Toroidal Meshes
- Patterns, Models, and Challenges in Online Social Media: A Survey
- How can social herding enhance cooperation?
- Methodology for Mining, Discovering and Analyzing Semantic Human Mobility Behaviors
- A note on temperature without energy - a social example
- Temperature Measurement in Agent Systems
- Peer influence breaks ergodicity in an opinion dynamics model with external information
- Opinion dynamics with confidence threshold: an alternative to the Axelrod model
- Bounded confidence dynamics and graph control: enforcing consensus
- Variational Inference with Agent-Based Models
- Sociophysics models inspired by the Ising model
- How the online social networks are used: Dialogs-based structure of MySpace
- The Impact of Network Flows on Community Formation in Models of Opinion Dynamics
- LLM-Based Social Simulations Require a Boundary
- Xenophobia based on a few attributes can impede society's cohesiveness
- How Large Language Models play humans in online conversations: a simulated study of the 2016 US politics on Reddit
- Unveiling Complex Territorial Socio-Economic Dynamics: A Statistical Mechanics Approach
- Market efficiency, anticipation and the formation of bubbles-crashes
- Modeling Earth-Scale Human-Like Societies with One Billion Agents
- Social physics
- Learning hidden influences in large-scale dynamical social networks: A data-driven sparsity-based approach
- A universal cutoff phenomenon for mean-field exchange models
- Coupled Ising models and interdependent discrete choices under social influence in homogeneous populations
- A Distributed, Dynamical System View of Finite, Static Games
- Understanding the Effect of Knowledge Graph Extraction Error on Downstream Graph Analyses: A Case Study on Affiliation Graphs
- Bias and Identifiability in the Bounded Confidence Model
- Dynamics of discrete opinions without compromise
- Probability of Consensus of Hegselmann-Krause Dynamics
- Ordering-disordering dynamics of the q-voter model under random external bias
- Activity Dynamics in Collaboration Networks
- Memory-Driven Bounded Confidence Opinion Dynamics: A Hegselmann-Krause Model Based on Fractional-Order Methods
- Emergence through Selection: The Evolution of a Scientific Challenge
- A data-driven model for Mass Media influence in electoral context
- Random walks with resetting on hypergraph
- Free Information Flow Benefits Truth Seeking
- The norm game on a model network: a critical line
- Simulating Opinion Dynamics in Heterogeneous Communication
- Probability of consensus in the multivariate Deffuant model on finite connected graphs
- Une étude de physique sur les élections
- The Evolution of Beliefs over Signed Social Networks
- Annealing approximation in master-node network model
- Bulk topological states in a new collective dynamics model
- Big data, bigger dilemmas: A critical review
- Context-Aware Sentiment Forecasting via LLM-based Multi-Perspective Role-Playing Agents
- Effects of higher-order interactions and homophily on information access inequality
- Opinions and dark energy: A mechanism of long-range repulsion in a toy opinion particle model
- Modeling the emergence of a new language: Naming Game with hybridization
- Does Having More Options Mean Harder to Reach Consensus?
- Synergistic effects in threshold models on networks
- The alignment model of indirect communication
- Further results on consensus formation in the Deffuant model
- Generalized Dynamics in Social Networks With Antagonistic Interactions
- Learning Individual Behavior in Agent-Based Models with Graph Diffusion Networks
- Consensus formation in networks with neighbor-dependent synergy and observer effect
- Opinion dynamics for an increasing population of agents. A symmetric continuous agent model
- A new degree of freedom for opinion dynamics models: the arbitrariness of scales
- Locating influential nodes via dynamics-sensitive centrality
- Modeling the life and death of competing languages from a physical and mathematical perspective
- Divestment may burst the carbon bubble if investors' beliefs tip to anticipating strong future climate policy
- Information spreading on dynamic social networks
- Natural selection of mutants that modify population structure
- Enhancing social cohesion with cooperative bots in societies of greedy, mobile individuals
- Collective group drift in a partial-differential-equation-based opinion dynamics model with biased perception kernels
- Evaluation and Control of Opinion Polarization and Disagreement: A Review
- Finite-Time Elimination of Disagreement of Opinion Dynamics via Covert Noise
- Agent-based simulations of emotion spreading in online social networks
- Opinion dynamics on a group structured adaptive network
- When cardinals strategize: An agent-based model of influence and ideology for the papal conclave
- AI Approaches to Qualitative and Quantitative News Analytics on NATO Unity
- An Information-Theoretic Formalism for Multiscale Structure in Complex Systems
- Universality of the SIS prevalence in networks
- Participation and Privacy perception in virtual environments: the role of sense of community, culture and sex between Italian and Turkish
- Probabilistic Cellular Automata: between deterministic Wolfram's rules 23, 77, 178 and 232
- Social Theory Should Be a Structural Prior for Agentic AI: A Formal Framework for Multi-Agent Social Systems
- When Is Collective Intelligence a Lottery? Multi-Agent Scaling Laws for Memetic Drift in LLMs
- Balanced and fragmented phases in societies with homophily and social balance
- Language Is a Complex Adaptive System: Position Paper
- Emergence of Biased Consensus in Multi-Agent LLM Debates
- The collective statistical mechanical personality of a group
- Threshold Learning Dynamics in Social Networks
- Emergence of target waves in paced populations of cyclically competing species
- Spatial correlations in vote statistics: a diffusive field model for decision-making
- Consensus versus persistence of disagreement in opinion formation: the role of zealots
- Impact of Human Activity Patterns on the Dynamics of Information Diffusion
- The physics of custody
- Infrequent social interaction can accelerate the spread of a persuasive idea
- Clustering of tag-induced subgraphs in complex networks
- In social complex systems, the whole can be more or less than (the sum of) the parts
- Gravity Effects on Information Filtering and Network Evolving
- Collective beliefs and individual stubbornness in the dynamics of public debates
- PageRank model of opinion formation on Ulam networks
- Coexistence in a one-dimensional cyclic dominance process
- Inertial Hegselmann-Krause Systems
- Evolution of ethnocentrism on undirected and directed Barabási–Albert networks
- What is a leader of opinion formation in bounded confidence models?
- Coarsening Dynamics of Binary Bose Condensates
- Analytical solution of the voter model on uncorrelated networks
- The statistical laws of popularity: universal properties of the box-office dynamics of motion pictures
- Variational principle underlying scale invariant social systems
- Evolution and Limiting Configuration of a Long-Range Schelling-Type Spin System
- Block-Fitness Modeling of the Global Air Mobility Network
- Information Is Not a Virus, and Other Consequences of Human Cognitive Limits
- Why, when, and how fast innovations are adopted
- Coarsening and Bifurcations in Wide-Range Two-Dimensional Totalistic Cellular Automata
- Percolation on complex networks: Theory and application
- Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections
- The emergence of consensus: a primer
- Epidemic spreading in multiplex networks influenced by opinion exchanges on vaccination
- SPONTANEOUS REORIENTATIONS IN A MODEL OF OPINION DYNAMICS WITH ANTICONFORMISTS
- A Biased Review of Sociophysics
- Phase transition in the Sznajd model with independence
- Voter model on the two-clique graph
- Information spreading and development of cultural centers
- You Name It – How Memory and Delay Govern First Name Dynamics
- Patterns, Entropy, and Predictability of Human Mobility and Life
- Time-Varying Graphs and Social Network Analysis: Temporal Indicators and Metrics
- The amplification of risk in experimental diffusion chains
- Conformity enhances network reciprocity in evolutionary social dilemmas
- Universal and nonuniversal features of the generalized voter class for ordering dynamics in two dimensions
- Emergence of polarized ideological opinions in multidimensional topic spaces
- Spectrum of controlling and observing complex networks
- Around the gap between sociophysics and sociology
- Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power
- Phase transitions in a two-parameter model of opinion dynamics with random kinetic exchanges
- Multi-parameter models of innovation diffusion on complex networks
- Usage bibliometrics
- Scale-invariance underlying the logistic equation and its social applications
- The nature of the continuous non-equilibrium phase transition of Axelrod's model
- Energy cost study for controlling complex social networks with conformity behavior
- Dynamics of Boltzmannian temporal difference reinforcement learning in social dilemmas
- Stochastic Non-Linear Influence in Synchronisation Dynamics
- Connect and win: The role of social networks in political elections
- Hysteresis and disorder-induced order in continuous kinetic-like opinion dynamics in complex networks
- Pólya Urn with Memory Kernel and Asymptotic Behaviors of Autocorrelation Function
- A stochastic evolutionary model generating a mixture of exponential distributions
- Memory-endowed US cities and their demographic interactions
- Opinion polarization by learning from social feedback
- Phase transitions and universality in the Sznajd model with anticonformity
- Nonequilibrium phase transition due to isolation of communities
- Quantum-mechanical machinery for rational decision-making in classical guessing game
- Mass media and heterogeneous bounds of confidence in continuous opinion dynamics
- Critical phenomena in the spreading of opinion consensus and disagreement
- A study on the effects of diffusion of information on epidemic spread
- Bifurcations in models of a society of reasonable contrarians and conformists
- Conformity-driven agents support ordered phases in the spatial public goods game
- Periodic coupling inhibits second-order consensus on networks
- Broken Detailed Balance and Non-Equilibrium Dynamics in Noisy Social Learning Models
- Temperature-induced collapse of spin dimensionality in magnetic metamaterials
- Nonlinearq-voter model
- Binary-State Dynamics on Complex Networks: Pair Approximation and Beyond
- Space Matters: extending sensitivity analysis to initial spatial conditions in geosimulation models
- Dynamics of epidemic spreading with vaccination: Impact of social pressure and engagement
- Transitions between polarization and radicalization in a temporal bilayer echo chambers model
- Networks maximizing the consensus time of voter models
- Evolution towards Linguistic Coherence in Naming Game with Migrating Agents
- Aging in Some Opinion Formation Models: A Comparative Study
- Diffusing opinions in bounded confidence processes
- An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics
- Spatial networks
- Irreducibility of multilayer network dynamics: the case of the voter model
- Epidemics with containment measures
- A Poissonian explanation for heavy tails in e-mail communication
- Dynamical Patterns of Cattle Trade Movements
- A note on the consensus time of mean-field majority-rule dynamics
- A convection–diffusion model for gang territoriality
- Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics
- Effects of population growth on the success of invading mutants
- Sustainable institutionalized punishment requires elimination of second-order free-riders
- Detection of Phase Transition in Generalized Pólya Urn in Information Cascade Experiment
- Social cycling and conditional responses in the Rock-Paper-Scissors game
- Moment-Closure Approximations for Discrete Adaptive Networks
- Binary-state dynamics on complex networks: Stochastic pair approximation and beyond
- MAJORITY-VOTE MODEL WITH HETEROGENEOUS AGENTS ON SQUARE LATTICE
- Evolution of autocatalytic sets in a competitive percolation model
- Noise Reduction in Coarse Bifurcation Analysis of Stochastic Agent-Based Models: An Example of Consumer Lock-In
- Towards the Heider balance: Cellular automaton with a global neighborhood
- Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges
- Generalized friendship paradox in networks with tunable degree-attribute correlation
- The web of connections between tourism companies: Structure and dynamics
- General three-state model with biased population replacement: Analytical solution and application to language dynamics
- Fragmentation transition in a coevolving network with link-state dynamics
- Persistent individual bias in a voter model with quenched disorder
- Mass media and repulsive interactions in continuous-opinion dynamics
- Multiplex networks of musical artists: The effect of heterogeneous inter-layer links
- Size distribution of cities: A kinetic explanation
- Socio-Economic Inequalities: A Statistical Physics Perspective
- Interdependent binary choices under social influence: Phase diagram for homogeneous unbiased populations
- Internet comments as a barometer of public opinion
- Bistability, non-ergodicity, and inhibition in pairwise maximum-entropy models
- Interplay between consensus and coherence in a model of interacting opinions
- Signs of universality in the structure of culture
- Fundamental ingredients for discontinuous phase transitions in the inertial majority vote model
- Maximizing Influence in an Ising Network: A Mean-Field Optimal Solution
- Time-varying priority queuing models for human dynamics
- Analysing and controlling the tax evasion dynamics via majority-vote model
- Classes of critical avalanche dynamics in complex networks
- Rumor propagation with heterogeneous transmission in social networks
- Consensus and polarization in competing complex contagion processes
- Non-Maxwellian kinetic equations modeling the evolution of wealth distribution
- Fitness voter model: Damped oscillations and anomalous consensus
- Flocking dynamics with voter-like interactions
- Approach to consensus in models of continuous-opinion dynamics: A study inspired by the physics of granular gases
- Opinion polarization in the Receipt–Accept–Sample model
- Influence of periodic external fields in multiagent models with language dynamics
- The role of noise in the spatial public goods game
- Complex societies and the growth of the law
- Interaction size and dissent tolerance in majority-rule dynamics with collective reversal
- Social diffusion and global drift on networks
- Stochastic Processes with Distributed Delays: Chemical Langevin Equation and Linear-Noise Approximation
- Formation of Scientific Fields as a Universal Topological Transition
- Patterns of Linguistic Diffusion in Space and Time: The Case of Mazatec
- Null-eigenvalue localization of quantum walks on complex networks
Discussions
Related