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We compare the decay rates of excited populations directly calculated within a Keldysh formalism to the equation of motion of the population itself for a Hubbard-Holstein model in two dimensions. While it is true that these two approaches…

Mesoscale and Nanoscale Physics · Physics 2016-05-25 Alexander F. Kemper , James. K. Freericks

Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…

Populations and Evolution · Quantitative Biology 2022-01-19 K. Bodova , E. Szep , N. H. Barton

Population dynamics reflects an underlying birth-death process, where the rates associated with different events may depend on external environmental conditions and on the population density. A whole family of simple and popular…

Populations and Evolution · Quantitative Biology 2019-07-03 Yitzhak Yahalom , Bnaya Steinmetz , Nadav M. Shnerb

We study the coupled dynamics of two populations of random replicators by means of statistical mechanics methods, and focus on the effects of relative population size, strategy correlations and heterogeneities in the respective co-operation…

Populations and Evolution · Quantitative Biology 2007-11-02 Tobias Galla

We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle…

Plasma Physics · Physics 2009-11-07 A. Chechkin , V. Gonchar , M. Szydlowski

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…

Statistical Mechanics · Physics 2007-05-23 Arne Traulsen , Jens Christian Claussen , Christoph Hauert

We examine the validity of the Fokker-Planck equation with linear force coefficients as an approximation to the kinetic equation of nucleation in homogeneous isothermal multicomponent condensation. Starting with a discrete equation of…

Classical Physics · Physics 2021-10-04 Yuri S. Djikaev , Eli Ruckenstein , Mark Swihart

We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one…

Statistical Mechanics · Physics 2009-11-10 Freddy Bouchet , Thierry Dauxois

In this paper, we consider an opioid epidemic dynamical model with random perturbation that typically describes the interplay between regular prescription use, addictive use, and the process of rehabilitation from addiction and vice-versa.…

Optimization and Control · Mathematics 2018-06-19 Getachew K. Befekadu , Quanyan Zhu

We study the evolution in time of the statistical distribution of some addiction phenomena in a system of individuals. The kinetic approach leads to build up a novel class of Fokker--Planck equations describing relaxation of the probability…

Physics and Society · Physics 2019-10-01 Giuseppe Toscani

We introduce and discuss a kinetic framework describing the time evolution of the statistical distributions of a population divided into the compartments of susceptible, infectious, recovered, and resistant in the presence of a microbial…

Populations and Evolution · Quantitative Biology 2026-05-07 Marco Menale , Giuseppe Toscani , Mattia Zanella

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

We present a nonequilibrium kinetic theory describing atom-molecule population dynamics in a two-component Fermi gas with a Feshbach resonance. Key collision integrals emerge that govern the relaxation of the atom-molecule mixture to…

Other Condensed Matter · Physics 2009-11-10 J. E. Williams , T. Nikuni , N. Nygaard , C. W. Clark

We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…

Optimization and Control · Mathematics 2018-11-14 Shui-Nee Chow , Wuchen Li , Jun Lu , Haomin Zhou

Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…

Populations and Evolution · Quantitative Biology 2020-07-22 Jayant Pande , Nadav M. Shnerb

The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…

Populations and Evolution · Quantitative Biology 2009-11-13 M. H. Vainstein , J. M. Rubi , J. M. G. Vilar

We study a system of Fokker-Planck equations recently introduced to describe the temporal evolution of statistical distributions of population densities with predator-prey interactions. At the macroscopic level, the system recovers a…

Analysis of PDEs · Mathematics 2026-03-11 Giuseppe Toscani , Mattia Zanella

Dynamics of complex systems is often hierarchically organized on different time scales. To understand the physics of such hierarchy, here Brownian motion of a particle moving through a fluctuating medium with slowly varying temperature is…

Statistical Mechanics · Physics 2014-02-14 Sumiyoshi Abe

We study the joint dynamics of membrane potential and time since the last spike in a population of integrate-and-fire neurons using a population density framework. This leads to a two-dimensional Fokker-Planck equation that captures the…

Disordered Systems and Neural Networks · Physics 2026-01-01 Luca Falorsi , Gianni V. Vinci , Maurizio Mattia

We derive general kinetic and hydrodynamic models of chemotactic aggregation that describe certain features of the morphogenesis of biological colonies (like bacteria, amoebae, endothelial cells or social insects). Starting from a…

Biological Physics · Physics 2009-11-13 Pierre-Henri Chavanis , Clement Sire