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We compare two approaches to nonequilibrium thermodynamics, the two-generator bracket formulation of time-evolution equations for averages and the macroscopic fluctuation theory, for an isothermal driven diffusive system under steady state…

Statistical Mechanics · Physics 2010-11-10 Hans Christian Ottinger

A recently introduced nonlinear Fokker-Planck equation, derived directly from a master equation, comes out as a very general tool to describe phenomenologically systems presenting complex behavior, like anomalous diffusion, in the presence…

Statistical Mechanics · Physics 2009-11-13 Veit Schwammle , Evaldo M. F. Curado , Fernando D. Nobre

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes one we developed previously (Phys. Rev. E v.79, 011110, 2009) in order to describe the Levy type stochastic processes in terms of continuous…

Statistical Mechanics · Physics 2015-05-13 Ihor Lubashevsky , Rudolf Friedrich , Andreas Heuer

We introduce a new class of stochastic processes which are stationary, Markovian and characterized by an infinite range of time-scales. By transforming the Fokker-Planck equation of the process into a Schrodinger equation with an…

Statistical Mechanics · Physics 2007-05-23 Fabrizio Lillo , Salvatore Micciche' , Rosario N. Mantegna

We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…

Optimization and Control · Mathematics 2024-09-23 Roman Chertovskih , Nikolay Pogodaev , Maxim Staritsyn , A. Pedro Aguiar

We study the Fokker-Planck equation derived in the large system limit of the Markovian process describing the dynamics of quantitative traits. The Fokker-Planck equation is posed on a bounded domain and its transport and diffusion…

Analysis of PDEs · Mathematics 2018-08-01 Katarina Bodova , Jan Haskovec , Peter Markowich

In this paper, we study the set of stationary solutions of the Vlasov-Fokker-Planck (VFP) equation. This equation describes the time evolution of the probability distribution of a particle moving under the influence of a double-well…

Analysis of PDEs · Mathematics 2015-08-11 Manh Hong Duong , Julian Tugaut

A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…

Statistical Mechanics · Physics 2008-08-08 Bohdan Lev

We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…

Statistical Mechanics · Physics 2015-06-18 Ying Tang , Ruoshi Yuan , Ping Ao

The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid…

Chaotic Dynamics · Physics 2014-04-30 Alexander V. Milovanov , Jens Juul Rasmussen

We prove the existence of weak solutions of a class of multi-species cross-diffusion systems as well as the propagation of chaos result by means of nonlocal approximation of the nonlinear diffusion terms, coupling methods and compactness…

Analysis of PDEs · Mathematics 2024-10-18 Jose Antonio Carrillo , Shuchen Guo

We consider the usual Langevin equation depending on an internal time. This parameter is substituted by a first passage time of a self-similar Markov process. Then the Gaussian process is parent, and the hitting time process is directing.…

Statistical Mechanics · Physics 2011-11-15 Aleksander Stanislavsky

This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…

Probability · Mathematics 2016-11-29 Erkan Nane , Yinan NI

This paper focuses on finding an approximate solution of a kind of Fokker-Planck equation with time-dependent perturbations. A formulation of the approximate solution of the equation is constructed, and then the existence of the formulation…

Probability · Mathematics 2025-09-12 Yan Luo , Kaicheng Sheng

We apply stochastic quantization method to matrix models for the second quantization of loops in both discretized and continuum levels. The fictitious time evolution described by the Langevin equation is interpreted as the time evolution in…

High Energy Physics - Theory · Physics 2009-10-28 N. Nakazawa

We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…

We prove global existence, uniqueness and regularity of the mild, Lp and classical solution of a non-linear Fokker-Planck equation arising in an adaptive importance sampling method for molecular dynamics calculations. The non- linear term…

Analysis of PDEs · Mathematics 2015-10-15 Houssam Alrachid , Tony Lelièvre , Raafat Talhouk

In this work, we develop novel structure-preserving numerical schemes for a class of nonlinear Fokker--Planck equations with nonlocal interactions. Such equations can cover many cases of importance, such as porous medium equations with…

Numerical Analysis · Mathematics 2020-08-18 Chenghua Duan , Wenbin Chen , Chun Liu , Xingye Yue , Shenggao Zhou

In this paper, we look at a probabilistic approach to a non-local quadratic form that has lately attracted some interest. This form is related to a recently introduced non-local normal derivative. The goal is to construct two Markov…

Probability · Mathematics 2019-09-25 Zoran Vondraček

Given a reaction-advection-diffusion system modelling the sulphation phenomenon, we derive a single regularised non-conservative and path-dependent nonlinear partial differential equation and propose a probabilistic interpretation via a…

Probability · Mathematics 2025-10-14 Daniela Morale , Leonardo Tarquini , Stefania Ugolini