Statistical mechanics of money

Numerical Simulation of Entropy Growth for a Nonlinear Evolutionary Model of Random Markets

Keshtkar, M., Navidi, H., & Shivanian, E. (2016) · Advances in Mathematical Physics · doi:10.1155/2016/2726394

Economics as a Science

Estola, M. (2017) · Springer eBooks · doi:10.1007/978-3-319-46879-2_1

A Poisson-like closed-form expression for the steady-state wealth distribution in a kinetic model of gambling

Garcia, J. B. D. M., & Esguerra, J. P. (2017) · AIP conference proceedings · doi:10.1063/1.4996529

Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange

Bertotti, M. L., Chattopadhyay, A. K., & Modanese, G. (2018) · Entropy · doi:10.3390/e20030166

Specifikace makroekonomického modelu z pohledu ekonofyziky

Sirotek, V. (2012) · Digital Library (University of West Bohemia)

Power accretion in social systems

Santalla, S. N., Koroutchev, K., Korutcheva, E., & Rodríguez-Laguna, J. (2019) · Physical review. E · doi:10.1103/physreve.100.012143

The Statistical Physics of A Private Ownership Society

Huato, J. (2019) · Science & Society · doi:10.1521/siso.2019.83.2.184

Agent-Based Model History and Development

Gooding, T. (2019) · Springer eBooks · doi:10.1007/978-3-030-17020-2_4

Mean-field limit for a collision-avoiding flocking system and the time-asymptotic flocking dynamics for the kinetic equation

Yang, R., Chen, L., & U. M. (2014) · Kinetic and Related Models · doi:10.3934/krm.2014.7.381

Measuring the Income Distribution

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.005

The Money Paradox

Kuntsevich, I. V., & Libkhen, R. V. (2020) · Journal of Business Theory and Practice · doi:10.22158/jbtp.v8n3p16

Computational Information Density and Entropy of the Bitcoin blockchain

Nesenberend, C. T. (2020) · Utrecht University Repository (Utrecht University)

Goodwin-Type Distributive Macrodynamics

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.011

Finding the Impact of Market Visibility and Monopoly on Wealth Distribution and Poverty Using Computational Economics

Zia, K., Farooq, U., & Ajmi, S. A. (2021) · Computational Economics · doi:10.1007/s10614-021-10201-x

Socio-Economic Modeling

Markowich, P. A., & Toscani, G. (2007) · Springer eBooks · doi:10.1007/978-3-540-34646-3_12

ESTUDO DA DINÂMICA ESTOCÁSTICA DE REDISTRIBUIÇÃO DA RIQUEZA USANDO UMA EQUAÇÃO DE FOKKER-PLANCK

LIMA, H. L. L. (2020) · doi:10.17771/pucrio.acad.50971

Piketty’s Capital in the Twenty-First Century

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.006

Stochastic Dynamics of Income and Wealth

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.008

Econophysics, Observational

Roehner, B. M. (2009) · Springer eBooks · doi:10.1007/978-1-4419-7701-4_13

Economic Cycles

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.009

Subject Index

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.012

Econophysics, Observational

Roehner, B. M. (2017) · Springer eBooks · doi:10.1007/978-3-642-27737-5_168-2

Basics

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.003

Preface

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.001

Author Index

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.013

Statistical Econophysics

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.007

Circular Flows in Economic Systems

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.010

Economics and Econophysics

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.004

Money Distribution

Gooding, T. (2019) · Springer eBooks · doi:10.1007/978-3-030-17020-2_8

Acknowledgements

Ribeiro, M. B. (2020) · Cambridge University Press eBooks · doi:10.1017/9781316136119.002

Peer Review #1 of "Age-related changes in the distributions of depressive symptom items in the general population: a cross-sectional study using the exponential distribution model (v0.1)"

(2016) · PeerJ · doi:10.7287/peerj.1547v0.1/reviews/1

Econophysics, Observational

Roehner, B. M. (2009) · Springer eBooks · doi:10.1007/978-0-387-30440-3_168

Power laws and symmetries in a minimal model of financial market economy

Ziyin, L., Ito, K., Imajo, K., & Minami, K. (2022) · Physical Review Research · doi:10.1103/physrevresearch.4.033077

Redistribution of Wealth: An Agent-based Simulation

GUNAWAN, F. E., & Riansah, F. (2021) · International Symposium on Materials and Electrical Engineering (ISMEE) · doi:10.1109/ismee54273.2021.9774097

Two Models of Speculative Bubbles Dynamics for Cryptocurrency Prices

Perepelitsa, M. (2022) · Applied Economics and Finance · doi:10.11114/aef.v9i4.5738

The Model of Socio-Economic Stratification of Society Based on An Agent Approach, Taking Into Account Rank Exchange

Капитанов, В. А., Osipova, O. S., & Maksimova, A. U. (2023) · Statistics and Economics · doi:10.21686/2500-3925-2023-1-4-23

Redes internas de suministro de Alemania y China y su influencia en los patrones de distribución del ingreso en el contexto de la crisis financiera de 2008

de Guadalajara, C. U., García, I. P. F., González, Á. M., de Guadalajara, C. U., Cervantes-Martínez, R., & de Guadalajara, C. U. (2023) · Expresión Económica · doi:10.32870/eera.vi50.1083

A Multi-Agent Description of Social Phenomena with Lognormal Equilibria

Toscani, G. (2022) · Springer INdAM series · doi:10.1007/978-981-19-6462-6_20

Application of the Deffuant Model in Money Exchange

Li, H.-L. (2025) · Communications in Mathematics and Applications · doi:10.26713/cma.v16i4.3124

Understanding Money Distribution in Closed Economic Systems: A Graph Theoretical Approach with Quantum Random Walks

Tsiatsios, G. A., Melas, E., Poulios, C., & Leventides, J. (2023) · International Conference on Industrial Artificial Intelligence (IAI) · doi:10.1109/iai59504.2023.10327576

Mapping the Parameter Space of Simulated Lotteries

Gere, I. (2023) · Journal of Social and Economic Statistics · doi:10.2478/jses-2023-0008

Essays on statistical equilibrium and competition in local public goods : philosophical explorations and empirical perspectives

Melo, J. (2022) · theses.fr (ABES) · doi:10.70675/4bbfdf35ze486z4321za0b5z6347b1017654

Desparekotasun globala, energiaren kontsumoa eta CO2-emisioak ekonofisikaren ikuspuntutik

Murgiondo, O. S., Manzano, H., & Martínez-Perdiguero, J. (2024) · EKAIA Euskal Herriko Unibertsitateko Zientzi eta Teknologi Aldizkaria · doi:10.1387/ekaia.24625

Sequential Bayesian Estimation

de Cursi, E. S. (2024) · International series in management science/operations research/International series in operations research & management science · doi:10.1007/978-3-031-48208-3_6

Information and Entropy

de Cursi, E. S. (2024) · International series in management science/operations research/International series in operations research & management science · doi:10.1007/978-3-031-48208-3_3

Maximum Entropy

de Cursi, E. S. (2024) · International series in management science/operations research/International series in operations research & management science · doi:10.1007/978-3-031-48208-3_4

Bayesian Inference

de Cursi, E. S. (2024) · International series in management science/operations research/International series in operations research & management science · doi:10.1007/978-3-031-48208-3_5

The Evolution of Exchange Process

Aruka, Y. (2024) · Springer texts in business and economics · doi:10.1007/978-981-97-1382-0_10

Wealth dynamics in a multi-aggregate closed monetary system

Monaco, A., Ghio, M., & Perrotta, A. (2024) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2024.129851

Analysis of financial markets by coupled criticality approach

Adeli, S., Namaki, A., Shirkavand, S., Tehrani, R., & Lai, Z. K. (2024) · International Journal of Modern Physics C · doi:10.1142/s012918312450181x

Estudio de la dinámica de préstamos y depósitos en un sistema económico cerrado a partir de modelos cinéticos de distribución

Niño, A. S., Osorio, W. A. A., & Martínez, J. L. A. (2024) · Cuadernos de Economía · doi:10.15446/cuad.econ.v43n91.99851

Progressive Income Tax and Its Emerging Growth Effects: A Complex System Approach

Álvarez, E., Álvez, M., & Brida, J. G. (2024) · IEEE Transactions on Computational Social Systems · doi:10.1109/tcss.2024.3418625

Early attempts to integrate kinetic theory into economics in Italy between the wars

Tusset, G. (2024) · European Journal of the History of Economic Thought · doi:10.1080/09672567.2024.2396860

A Dive Into the Asymptotic Analysis Theory: a Short Review from Fluids to Financial Markets

Sbaiz, G. (2024) · Acta Mathematicae Applicatae Sinica English Series · doi:10.1007/s10255-024-1144-1

Use of Euler’s theorem in the elucidation of economic concepts in goods exchange

Villegas-Febres, J. C. (2025) · International Journal of Modern Physics C · doi:10.1142/s0129183125500846

The multilayer garbage disposal game

Li, H. (2025) · The Journal of Difference Equations and Applications · doi:10.1080/10236198.2025.2508899

A Non-Conservative Kinetic Framework for EconophysicsPreprint

Lee, K. (2025) · SSRN Electronic Journal · doi:10.2139/ssrn.5385848

MyWealth: A Simple Model of Economic Exchange in Python

Margarido, J., & Campos, P. (2025) · Springer eBooks · doi:10.1007/978-3-031-73354-3_6

Tuning the Probabilistic Distribution and the Gini Index

Khorrami, M. (2025) · Brazilian Journal of Physics · doi:10.1007/s13538-025-01879-7

Mind Your Threes and Twos

Dorée, S., Hanson, R. M., & Richey, M. P. (2025) · Mathematics Magazine · doi:10.1080/0025570x.2025.2506963

Temporal Fluctuation Scaling and Temporal Theil Scaling in Financial Time Series

Bermúdez, F. S. A., & Quimbay, C. J. (2025) · Springer eBooks · doi:10.1007/978-3-031-84782-0_17

Discrete Boltzmann distributions via multisets and their coefficientsPreprint

Jacobs, B. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2507.05719

Mean-Field Analytical Solution of the Mesa Boltzmann Wealth ModelPreprint

Lyu, J. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2511.08202

Bioeconophysical science of microeconomical equilibrium of stocks

Petrov, M., & Tranev, S. (2025) · Journal of Physics Conference Series · doi:10.1088/1742-6596/3145/1/012037

Effect of Markets Temperature on Stock-Price: Monte Carlo Simulation on Spin Model

Thongon, A., Sriboonchitta, S., & Laosiritaworn, Y. (2013) · Advances in intelligent systems and computing · doi:10.1007/978-3-319-03395-2_28

A Perspective for Analyzing the Socio-Economic System and Interactive Human Behaviour

Aruka, Y. (2011) · Physica-Verlag eBooks · doi:10.1007/978-3-7908-2618-0_1

Biswas–Chatterjee–Sen (BChS) kinetic exchange opinion model on modular networks

Unni, H., Biswas, S., & Chakraborti, A. (2026) · The European Physical Journal B · doi:10.1140/epjb/s10051-026-01273-5

Institutional Transformation of Zakat Towards a Maqashid Shariah-Based Distribution System and Econophysics Model: A Critical Conceptual Study from an Islamic Economic Perspective

Fitriah, M. (2025) · Islamic Banking and Finance Review · doi:10.32350/ibfr.122.04

Threshold Resource Redistribution in Spatially-Structured Kinship NetworksPreprint

Kochocki, A. (2026) · arXiv (Cornell University) · doi:10.48550/arxiv.2602.06200

Threshold Resource Redistribution in Spatially-Structured Kinship NetworksPreprint

Kochocki, A. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6271050

Crofton Risk and Relative Transactional Entropy

Makowski, M., & Piotrowski, E. W. (2026) · Entropy · doi:10.3390/e28020244

Statistical physics of an asset exchange model with investment and guaranteed income

Tobochnik, J., Gould, H., & Klein, W. (2026) · Physical review. E · doi:10.1103/2mh9-nn23

Wealth Redistribution and Strategic Behavior under Delayed Retirement: A Fokker–Planck and Mean-Field Game Approach

Jin, Y., & Lai, C. (2026) · Computational Economics · doi:10.1007/s10614-026-11342-7

A Non-Conservative Kinetic Framework for EconophysicsPreprint

Lee, K. (2026) · SSRN Electronic Journal · doi:10.2139/ssrn.6462005

Kardar-Parisi-Zhang universality in the phase of a condensate of exciton polaritons : from the scaling of correlation functions to advanced statistics of the phase in 1+1 and 2+1 dimensions

Deligiannis, K. (2022) · theses.fr (ABES) · doi:10.70675/7775af7ezcf64z4f24z97d0z3d11a546c7b6

Understanding financial contagion during crisis via a non-linear pricing model

Massad, N. (2022) · theses.fr (ABES) · doi:10.70675/da8fc9abz2217z492dzbb18zf8ee50b43852

Model Transfer as a Case of Interdisciplinary Research in Science

Herfeld, C. S., & Peruzzi, E. (2026) · Springer eBooks · doi:10.1007/978-981-92-2821-8_8

Testing the thermodynamics of order-book economies

Padigala, A., & MacKay, R. S. (2026) · Journal of Physics Complexity · doi:10.1088/2632-072x/aea987

Evolution of Money Distribution in a Simple Economic Model

Liang, X., & Carter, T. J. (2011) · Springer eBooks · doi:10.1007/978-3-642-17635-7_27

Порівняльний аналіз архітектур на основі великих мовних моделей та детермінованих алгоритмів у багатоагентних системах

Макаренко, В. Ю. (2026) · Електронний архів наукових та освітніх матеріалів КПІ ім. Ігоря Сікорського (КПІ ім. Ігоря Сікорського)

A new model for the income distribution

Aydıner, E. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.132084

Statistical mechanics of ideal economic systems

Akao, A. (2026) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2026.132140

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