Statistical mechanics of money

The econ in econophysics

Shaikh, A. M. (2020) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2020-900204-5 · Cited by 7

A Simple Mechanism Causing Wealth Concentration

Cieśla, M., & Snarska, M. (2020) · Entropy · doi:10.3390/e22101148 · Cited by 7

A multi-agent approach to the impact of epidemic spreading on commercial activities

Toscani, G. (2022) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202522500440 · Cited by 7

Antipersistent dynamics in kinetic models of wealth exchange

Goswami, S., Chatterjee, A., & Sen, P. (2011) · Physical Review E · doi:10.1103/physreve.84.051118 · Cited by 7

Economic exchanges in a stratified society: End of the middle class?

Laguna, M. F., Risau-Gusman, S., & Iglesias, J. R. (2005) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2005.05.021 · Cited by 7

A new κ -deformed parametric model for the size distribution of wealth

Vallejos, A., Ormazábal, I., Borotto, F. A., & Astudillo, H. F. (2018) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.09.060 · Cited by 7

Taxation of Wealthy Individuals, Inequality Governance and Corporate Social Responsibility

Chen, K., Lee, C., & Tsai, H. (2019) · Sustainability · doi:10.3390/su11071851 · Cited by 7

The effect of various tax and redistribution models on the Gini coefficient of simple exchange games

Kulp, C. W., Kurtz, M. D., Wilston, N., & Quigley, L. (2019) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.5110487 · Cited by 7

Economic Segregation Under the Action of Trading Uncertainties

Ballante, E., Bardelli, C., Zanella, M., Figini, S., & Toscani, G. (2020) · Symmetry · doi:10.3390/sym12091390 · Cited by 7

Mean-field theory of an asset exchange model with economic growth and wealth distribution

Klein, W., Lubbers, N., Liu, K. K. L., Khouw, T., & Gould, H. (2021) · Physical review. E · doi:10.1103/physreve.104.014151 · Cited by 7

Equiprobability, Entropy, Gamma Distributions and Other Geometrical Questions in Multi-Agent Systems

López‐Ruiz, R., Jaime Sañudo, A., & Calbet, X. (2009) · Entropy · doi:10.3390/e11040959 · Cited by 7

Coupled Criticality Analysis of Inflation and Unemployment.Preprint

Lai, Z. K., Namaki, A., Hosseiny, A., Jafari, G., & Ausloos, M. (2020) · RePEc: Research Papers in Economics · Cited by 7

Wealth Redistribution and Mutual Aid: Comparison Using Equivalent/Non-Equivalent Exchange Models of Econophysics

Kato, T. (2023) · Entropy · doi:10.3390/e25020224 · Cited by 6

Effects of consumption strategy on wealth distribution on scale-free networks

Pei, S., Tang, S., Zhang, X., Liu, Z., & Zheng, Z. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.10.017 · Cited by 6

Rethinking exchange market models as optimization algorithms

Luquini, E., & Omar, N. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.08.150 · Cited by 6

A poor agent and subsidy: an investigation through CCM model

Goswami, S. (2022) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2021.0166 · Cited by 6

Sticky Dispersion on the Complete Graph: A Kinetic Approach

Cao, F., & Motsch, S. (2025) · SIAM Journal on Mathematical Analysis · doi:10.1137/24m1654622 · Cited by 6

Statistical premium in correlated losses of insurance

Lai, L.-H. (2015) · Economic Modelling · doi:10.1016/j.econmod.2015.05.002 · Cited by 6

Inequality measures for wealth distribution: Population vs individuals perspective

Pascoal, R., & Rocha, H. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.11.059 · Cited by 6

Pattern formation in time series systems due to viscoelastic behavior: Case studies in uniform distribution, normal distribution, stock market index, and music

Gündüz, G. (2018) · International Journal of Modern Physics C · doi:10.1142/s0129183118500857 · Cited by 6

A toy model for the epidemic-driven collapse in a system with limited economic resource

Gandzha, I. S., Kliushnichenko, O. V., & Lukyanets, S. P. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00099-7 · Cited by 6

A multi-agent description of the influence of higher education on social stratification

Dimarco, G., Toscani, G., & Zanella, M. (2022) · Journal of Economic Interaction and Coordination · doi:10.1007/s11403-022-00358-5 · Cited by 6

Universal Pareto laws in agent-based exchange models: debt and varying initial-money distributions

Aydıner, E., Cherstvy, A. G., Metzler, R., & Sokolov, I. M. (2023) · The European Physical Journal B · doi:10.1140/epjb/s10051-023-00579-y · Cited by 6

Wealth Redistribution in Boltzmann-like Models of Conservative Economies

Toscani, G., & Brugna, C. (2010) · New economic windows · doi:10.1007/978-88-470-1501-2_9 · Cited by 6

From Sustainable Production to Sustainable Consumption

Wolf, M., & Chomkhamsri, K. (2015) · LCA compendium · doi:10.1007/978-94-017-7221-1_13 · Cited by 6

An almost linear stochastic map related to the particle system models of social sciences

Chakrabarti, A. S. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.06.080 · Cited by 6

Consequences of increased longevity for wealth, fertility, and population growth

Bogojević, A., Balaž, A., & Karapandža, R. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.09.004 · Cited by 6

Effects of taxation on money distribution

Diniz, M. A., & Mendes, F. M. (2011) · International Review of Financial Analysis · doi:10.1016/j.irfa.2011.06.014 · Cited by 6

Quantitative description of realistic wealth distributions by kinetic trading models

Lammoglia, N. L., Muñoz, V., Rogan, J. A., Toledo, B. A., Zarama, R., & Valdivia, J. A. (2008) · Physical Review E · doi:10.1103/physreve.78.047103 · Cited by 6

Statistical mechanics of a time-homogeneous system of money and antimoney

Schmitt, M., Schacker, A., & Braun, D. (2014) · New Journal of Physics · doi:10.1088/1367-2630/16/3/033024 · Cited by 6

Income distribution in the Colombian economy from an econophysics perspective

Quevedo, H., & Quevedo, M. N. (2016) · Cuadernos de Economía · doi:10.15446/cuad.econ.v35n69.44876 · Cited by 6

Boltzmann-type models for price formation in the presence of behavioral aspects

Brugna, C., & Toscani, G. (2015) · Networks and Heterogeneous Media · doi:10.3934/nhm.2015.10.543 · Cited by 6

Role of intensive and extensive variables in a soup of firms in economy to address long run prices and aggregate data

Hosseiny, A., & Gallegati, M. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.11.130 · Cited by 6

Viscoelasticity and pattern formations in stock market indices

Gündüz, G., & Gündüz, A. (2017) · The European Physical Journal B · doi:10.1140/epjb/e2017-70711-x · Cited by 6

The evolution of the exchange process: from the decentralized to the distributed digital exchange

Aruka, Y. (2020) · Evolutionary and Institutional Economics Review · doi:10.1007/s40844-020-00183-0 · Cited by 6

The Many Faces of Agent-Based Computational Economics: Ecology of Agents, Bottom-Up Approaches and Paradigm Shift

Mignot, S., & Vignes, A. (2019) · OEconomia · doi:10.4000/oeconomia.8222 · Cited by 6

Modeling and controlling the spread of epidemic with various social and economic scenarios

Gandzha, I. S., Kliushnichenko, O. V., & Lukyanets, S. P. (2021) · Chaos Solitons & Fractals · doi:10.1016/j.chaos.2021.111046 · Cited by 6

Wealth distribution of simple exchange models coupled with extremal dynamics

Bagatella-Flores, N., Rodríguez-Achach, M., Coronel-Brizio, H. F., & Hernández-Montoya, R. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.07.081 · Cited by 6

Wealth Distribution in a Network with Correlations Between Links and Success

Risau-Gusman, S., Laguna, M. F., & Iglesias, J. R. (2005) · New economic windows · doi:10.1007/88-470-0389-x_15 · Cited by 6

Wealth Distribution in Scale-Free Networks

Souma, W., Fujiwara, Y., & Aoyama, H. (2003) · Springer eBooks · doi:10.1007/978-4-431-67863-2_3 · Cited by 6

Power-law behavior and condensation phenomena in disordered urn models

Inoue, J., & Ohkubo, J. (2008) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/41/32/324020 · Cited by 6

Agent-based models of the United States wealth distribution with Ensemble Kalman Filter

Oswald, Y., Suchak, K., & Malleson, N. (2024) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2024.106820 · Cited by 5

DIRECTED RANDOM MARKETS: CONNECTIVITY DETERMINES MONEY

MARTÍNEZ-MARTÍNEZ, I., & López‐Ruiz, R. (2012) · International Journal of Modern Physics C · doi:10.1142/s012918311250088x · Cited by 5

Discrete hierarchy of sizes and performances in the exchange-traded fund universe

Vandermarliere, B., Ryckebusch, J., Schoors, K. J. L., Cauwels, P. P., & Sornette, D. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.11.084 · Cited by 5

Emergent inequality and self-organized social classes in a network of power and frustration

Mahault, B., Saxena, A., & Nisoli, C. (2017) · PLoS ONE · doi:10.1371/journal.pone.0171832 · Cited by 5

Consensus in complex networks with noisy agents and peer pressure

Griffin, C. H., Squicciarini, A., & Jia, F. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.128263 · Cited by 5

The interactive impact of green supporting factors on bank credit creation: An agent-based stock-flow consistent approach

Xing, X., Gu, X., Kun, G., & Deng, J. (2023) · The North American Journal of Economics and Finance · doi:10.1016/j.najef.2023.101994 · Cited by 5

Kinetic Exchange Models as D Dimensional Systems: A Comparison of Different Approaches

Patriarca, M., Heinsalu, E., Singh, A., & Chakraborti, A. (2017) · New economic windows · doi:10.1007/978-3-319-47705-3_11 · Cited by 5

Statistical Teleodynamics: Toward a Theory of Emergence

Venkatasubramanian, V. (2017) · Langmuir · doi:10.1021/acs.langmuir.7b02166 · Cited by 5

The Potential of Econophysics for the Study of Economic Processes

Săvoiu, G., & Andronache, C. (2013) · Elsevier eBooks · doi:10.1016/b978-0-12-404626-9.00007-4 · Cited by 5

Inequality and risk aversion in economies open to altruistic attitudes

Perversi, E., & Regazzini, E. (2016) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202516500433 · Cited by 5

Evolution of consumption distribution and model of wealth distribution in China between 1995 and 2012

Gao, L. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.02.067 · Cited by 5

Absorbing phase transition in energy exchange models

Basu, U., Basu, M., & Mohanty, P. K. (2013) · The European Physical Journal B · doi:10.1140/epjb/e2013-31129-x · Cited by 5

Numerical tools for obtaining power-law representations of heavy-tailed datasets

Mansfield, M. L. (2016) · The European Physical Journal B · doi:10.1140/epjb/e2015-60452-3 · Cited by 5

Kinetic theory and Brazilian income distribution

Siciliani, I. D. S., & Tragtenberg, M. H. R. (2018) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.08.164 · Cited by 5

Duality in an asset exchange model for wealth distribution

Li, J., & Boghosian, B. M. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2017.12.068 · Cited by 5

Scaling in local to global condensation of wealth on sparse networks

Lee, H. G., & Lee, D. (2023) · Physical review. E · doi:10.1103/physreve.108.064303 · Cited by 5

Kinetic Exchange Models in Economics and Sociology

Goswami, S., & Chakraborti, A. (2015) · Springer proceedings in mathematics & statistics · doi:10.1007/978-3-319-12328-8_4 · Cited by 5

Ideal-Gas Like Markets: Effect of Savings

Chatterjee, A., & Chakrabarti, B. K. (2005) · New economic windows · doi:10.1007/88-470-0389-x_9 · Cited by 5

The Microscopic Origin of the Pareto Law and Other Power-Law Distributions

Patriarca, M., Heinsalu, E., Chakraborti, A., & Kaski, K. K. (2017) · New economic windows · doi:10.1007/978-3-319-47705-3_12 · Cited by 5

Statistical Prediction of the Outcome of a Noncooperative GamePreprint

Wolpert, D. H., & Bono, J. W. (2008) · SSRN Electronic Journal · doi:10.2139/ssrn.1184325 · Cited by 5

Economic Models with Chaotic Money Exchange

Pellicer-Lostao, C., & López‐Ruiz, R. (2009) · Lecture notes in computer science · doi:10.1007/978-3-642-01970-8_5 · Cited by 5

Black Scholes Option Pricing Model – Brownian Motion ApproachPreprint

Prabakaran, S. (2014) · SSRN Electronic Journal · doi:10.2139/ssrn.2508148 · Cited by 5

Finite-time flocking with collision-avoiding problem of a modified Cucker-Smale model

Zhang, H., Yang, S., Zhao, R., & Liu, Q. (2022) · Mathematical Biosciences & Engineering · doi:10.3934/mbe.2022483 · Cited by 4

Toy models, dispositions, and the power to explain

Verreault-Julien, P. (2023) · Synthese · doi:10.1007/s11229-023-04084-8 · Cited by 4

Evolution of temporal fluctuation scaling exponent in nonstationary time series using supersymmetric theory of stochastic dynamics

Abril, F. S., & Quimbay, C. J. (2024) · Physical review. E · doi:10.1103/physreve.109.024112 · Cited by 4

Nonequilibrium statistical mechanics of money/energy exchange models

Miao, M., Makarov, D. E., & Blom, K. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad369b · Cited by 4

Inequality in a model of capitalist economy

de Borba, J. S., Gonçalves, S., & Anteneodo, C. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.130457 · Cited by 4

Intermittency in the integrated power of ionospheric density fluctuations

Ghadjari, H., Knudsen, D. J., Balasis, G., & Skone, S. H. (2025) · Journal of Space Weather and Space Climate · doi:10.1051/swsc/2025026 · Cited by 4

Quantitative convergence guarantees for the mean-field dispersion process

Cao, F., & Yang, J. (2025) · Discrete and Continuous Dynamical Systems · doi:10.3934/dcds.2025126 · Cited by 4

From Gini index as a Lyapunov functional to convergence in Wasserstein distance

Cao, F. (2026) · Statistics & Probability Letters · doi:10.1016/j.spl.2026.111001 · Cited by 4

Ab Initio Analysis of All Income Society Classes in the European Union

Jagielski, M., & Kutner, R. (2013) · Acta Physica Polonica A · doi:10.12693/aphyspola.123.538 · Cited by 4

Kinetic model of mass exchange with dynamic Arrhenius transition rates

Hristopulos, D. T., & Muradova, A. D. (2015) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2015.10.007 · Cited by 4

On the relationship between income, fertility rates and the state of democracy in society

Hutzler, S., Sommer, C., & Richmond, P. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.02.011 · Cited by 4

Wealth condensation in a Barabasi–Albert network

Vázquez-Montejo, J., Huerta-Quintanilla, R., & Rodríguez-Achach, M. (2009) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2009.12.013 · Cited by 4

Insights into the Macroscopic Behavior of Equity Markets: Theory and Application

AlShelahi, A., & Saigal, R. (2017) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2018.03.074 · Cited by 4

Stability of a time-homogeneous system of money and antimoney in an agent-based random economy

Stein, J., & Braun, D. (2019) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2019.01.022 · Cited by 4

The effects of taxes on wealth inequality in Artificial Chemistry models of economic activity

Banzhaf, W. (2021) · PLoS ONE · doi:10.1371/journal.pone.0255719 · Cited by 4

Wealth Rheology

Burda, Z., Krawczyk, M. J., Malarz, K., & Snarska, M. (2021) · Entropy · doi:10.3390/e23070842 · Cited by 4

Constructing games on networks for controlling the inequalities in the capital distribution

Miszczak, J. A. (2022) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2022.126997 · Cited by 4

Wealth distribution for agents with spending propensity, interacting over a network

Muñoz, V. (2022) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/5.0120979 · Cited by 4

Themes and Applications of Kinetic Exchange Models: Redux

Ghosh, A., Chakrabarti, A. S., Chandra, A. K., & Chakraborti, A. (2013) · New economic windows · doi:10.1007/978-3-319-00023-7_6 · Cited by 4

Dynamic Process of Money Transfer Models

Wang, Y., & Ding, N. (2005) · New economic windows · doi:10.1007/88-470-0389-x_13 · Cited by 4

Unhedgeable shocks and statistical economic equilibrium

Smith, E., Foley, D. K., & Good, B. H. (2011) · Economic Theory · doi:10.1007/s00199-011-0663-1 · Cited by 4

Employment, Production and Consumption model: Patterns of phase transitions

Lavička, H., Lin, L., & Novotný, J. (2010) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2009.12.046 · Cited by 4

Why only few are so successful?

Mohanty, P. K. (2007) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2007.04.118 · Cited by 4

Microscopic and kinetic models in financial markets

Cordier, S., Maldarella, D., Pareschi, L., & Piatecki, C. (2010) · Modeling and simulation in science, engineering & technology · doi:10.1007/978-0-8176-4946-3_3 · Cited by 4

Physicists’ Approaches to a Few Economic Problems

Chakraborti, A., Fujiwara, Y., Ghosh, A., Inoue, J., & Sitabhra Sinha, A. (2015) · New economic windows · doi:10.1007/978-3-319-08473-2_11 · Cited by 4

Building theories of economic process

Shubik, M., & Smith, E. (2008) · Complexity · doi:10.1002/cplx.20265 · Cited by 4

Relaxation in the wealth exchange models

Gupta, A. K. (2008) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2008.09.003 · Cited by 4

Money circulation and debt circulation: A restatement of quantity theory of money

Xing, X., Xiong, W., Chen, L., Chen, J., Wang, Y., & Stanley, E. (2018) · Econstor (Econstor) · Cited by 4

Exponential wealth distribution in a random market. A rigorous explanation

López, J. L., López‐Ruiz, R., & Calbet, X. (2011) · Journal of Mathematical Analysis and Applications · doi:10.1016/j.jmaa.2011.07.060 · Cited by 3

Velocity, Holding Time and Lifespan of Cryptocurrency in Transactions

Zhang, Y., Chegeni, M., & Tessone, C. J. (2024) · Lecture notes in operations research · doi:10.1007/978-3-031-68974-1_15 · Cited by 3

Thermodynamic Description of Wealth Inequality in the World

Frahm, K. M., Ermann, L., & Shepelyansky, D. L. (2026) · Complexities · doi:10.3390/complexities2030020 · Cited by 3

Mean-Field Analysis of a Random Asset Exchange Model with Probabilistic Cheaters

Cao, F. (2026) · SIAM Journal on Applied Mathematics · doi:10.1137/25m1786830 · Cited by 3

Income distribution: An adaptive heterogeneous model

da Silva, L. C., & de Figueirêdo, P. H. (2013) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2013.09.065 · Cited by 3

Market clearing by maximum entropy in agent models of stock markets

Wagner, F. (2011) · Journal of Economic Interaction and Coordination · doi:10.1007/s11403-011-0079-9 · Cited by 3

Clausius inequality and H -theorems for some models of random wealth exchange

Apenko, S. M. (2014) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2014.07.017 · Cited by 3

Exploring the Social-Architecture Model

Isaac, A. G. (2018) · Eastern Economic Journal · doi:10.1057/s41302-018-0114-9 · Cited by 3

Profitability, efficiency, and inequality in double auction markets with snipers

Brewer, P., & Ratan, A. (2019) · Journal of Economic Behavior & Organization · doi:10.1016/j.jebo.2019.06.017 · Cited by 3

XXXI Encontro Nacional de F́ısica da Matéria Condensada / ID: 862-1 1 Statistical Mechanics of Money in a Closed Economic System

Gomes, R. A., & Leão, S. D. A. (2014)

Statistical mechanics approach to the probability distribution of moneyPreprint

Yakovenko, V. M. (2010) · RePEc: Research Papers in Economics · doi:10.48550/arxiv.1007.5074 · Cited by 17

Nonequilibrium statistical mechanics of money/energy exchange models

Miao, M., Makarov, D. E., & Blom, K. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad369b · Cited by 4

ContentsPreprint

Yakovenko, V. M., & Rosser, J. B. (2009)

Colloquium : Statistical mechanics of money, wealth, and income

Yakovenko, V. M., & Rosser, J. B. (2009) · Reviews of Modern Physics · doi:10.1103/revmodphys.81.1703 · Cited by 559