English
Related papers

Related papers: Boltzmann legacy and wealth distribution

200 papers

Statistical models of economic distributions lead to Boltzmann distributions rather than a Pareto power law. This result is supported by two facts: 1. the distributions of income, car sales, marriages or jobs are a matter of chances and…

Statistical Mechanics · Physics 2008-12-02 J. Mimkes , Th. Fruend , G. Willis

We consider the kinetic theory of the quantum and classical Toda lattice models. A kinetic equation of Bethe-Boltzmann type is derived for the distribution function of conserved quasiparticles. Near the classical limit, we show that the…

Statistical Mechanics · Physics 2019-07-23 Vir B. Bulchandani , Xiangyu Cao , Joel E. Moore

An equation for the evolution of the distribution of wealth in a population of economic agents making binary transactions with a constant total amount of "money" has recently been proposed by one of us (RLR). This equation takes the form of…

Adaptation and Self-Organizing Systems · Physics 2014-07-29 Yves Pomeau , Ricardo Lopez-Ruiz

We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space - discrete time version of this model and, under suitable scaling, we show its functional…

Probability · Mathematics 2024-03-26 Bertram Düring , Nicos Georgiou , Sara Merino-Aceituno , Enrico Scalas

Boltzmann kinetic equation is put into the form of an abstract time evolution equation representing links connecting autonomous mesoscopic dynamical theories involving varying amount of details. In the chronological order we present results…

Statistical Mechanics · Physics 2023-04-12 Miroslav Grmela

Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock…

General Finance · Quantitative Finance 2017-02-10 M. L. Bertotti , A. K. Chattopadhyay , G. Modanese

Increasingly, a huge amount of statistics have been gathered which clearly indicates that income and wealth distributions in various countries or societies follow a robust pattern, close to the Gibbs distribution of energy in an ideal gas…

General Finance · Quantitative Finance 2009-11-13 Arnab Chatterjee , Bikas K. Chakrabarti

We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac's model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic…

Probability · Mathematics 2016-05-05 Roberto Cortez , Joaquin Fontbona

In this communication, complex systems with a near trivial dynamics are addressed. First, under the hypothesis of equiprobability in the asymptotic equilibrium, it is shown that the (hyper) planar geometry of an $N$-dimensional multi-agent…

Adaptation and Self-Organizing Systems · Physics 2012-10-25 Ricardo Lopez-Ruiz

We study a minimalist kinetic model for economies. A system of agents with local trading rules display emergent demand behaviour. We examine the resulting wealth distribution to look for non-thermal behaviour. We compare and contrast this…

General Finance · Quantitative Finance 2008-12-02 Wan Ahmad Tajuddin Wan Abdullah , Sidiq Mohamad Khidzir

We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…

Statistical Mechanics · Physics 2026-05-26 Weicheng Fu , Yisen Wang , Yong Zhang , Hong Zhao

Some general features of kinetic multi-agent models are reviewed, with particular attention to the relation between the agent saving propensities and the form of the equilibrium wealth distribution. The effect of a finite cutoff of the…

Physics and Society · Physics 2013-03-19 Marco Patriarca , Anirban Chakraborti , Guido Germano

In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator-prey interactions. The model builds upon the classical Boltzmann-type equations, where the…

Analysis of PDEs · Mathematics 2025-11-27 Andrea Bondesan , Marco Menale , Giuseppe Toscani , Mattia Zanella

The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied…

Analysis of PDEs · Mathematics 2022-03-08 Thierry Bodineau , Isabelle Gallagher , Laure Saint-Raymond , Sergio Simonella

Nonlinear kinetic equations are reviewed for a wide audience of specialists and postgraduate students in physics, mathematical physics, material science, chemical engineering and interdisciplinary research. Contents: The Boltzmann equation,…

Statistical Mechanics · Physics 2007-05-23 A. N. Gorban , I. V. Karlin

We study the kinetic theory of a weakly interacting quantum field. Assuming a state that is close to homogeneous and stationary, we derive a closed kinetic equation for the rate of change of the occupation numbers, perturbatively in the…

High Energy Physics - Theory · Physics 2025-09-03 Xu-Yao Hu , Vladimir Rosenhaus

The existence of stationary distributions in a multicomponent Boltzmann equation using a non-additive kinetic energy composition rule for binary collisions is discussed. It is found that detailed balance is not achieved when -- in contrast…

Statistical Mechanics · Physics 2014-08-19 M. Horváth , T. S. Biró

We study a stochastic $N$-particle system representing economic agents in a population randomly exchanging their money, which is associated to a class of one-dimensional kinetic equations modelling the evolution of the distribution of…

Probability · Mathematics 2018-09-17 Roberto Cortez

We analyze wealth condensation for a wide class of stochastic economy models on the basis of the economic analog of thermodynamic potentials, termed transfer potentials. The economy model is based on three common transfers modes of wealth:…

Physics and Society · Physics 2009-11-11 Dieter Braun

We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…

Mathematical Physics · Physics 2023-02-23 Marzia Bisi , Nadia Loy