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We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…

Statistical Mechanics · Physics 2015-06-18 A. Donev , T. G. Fai , E. Vanden-Eijnden

The problem of anomalous diffusion in momentum (velocity) space is considered based on the master equation and the appropriate probability transition function (PTF). The approach recently developed by the author for coordinate space, is…

Statistical Mechanics · Physics 2015-05-18 S. A. Trigger

Diffusion theory establishes a fundamental connection between stochastic differential equations and partial differential equations. The solution of a partial differential equation known as the Fokker-Planck equation describes the…

Probability · Mathematics 2025-10-24 Carlos Escudero , Helder Rojas

Starting from first principles, we formulate a theory of wave packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic…

Disordered Systems and Neural Networks · Physics 2011-10-28 Nicolas Cherroret , Thomas Wellens

We consider fluctuations of the dissipated energy in nonlinear driven diffusive systems subject to bulk dissipation and boundary driving. With this aim, we extend the recently-introduced macroscopic fluctuation theory to nonlinear driven…

Statistical Mechanics · Physics 2013-10-29 P. I. Hurtado , A. Lasanta , A. Prados

Recently a new type of Kramers-Fokker-Planck Equation has been proposed [R. Friedrich et al. Phys. Rev. Lett. {\bf 96}, 230601 (2006)] describing anomalous diffusion in external potentials. In the present paper the explicit cases of a…

Statistical Mechanics · Physics 2007-05-23 S. Eule , R. Friedrich , F. Jenko

A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…

Statistical Mechanics · Physics 2007-05-23 Jean Pierre Boon , Patrick Grosfils , James F. Lutsko

Memory effects require for their incorporation into random-walk models an extension of the conventional equations. The linear Fokker-Planck equation for the probability density $p(\vec r, t)$ is generalized to include non-linear and…

Statistical Mechanics · Physics 2009-11-10 Steffen Trimper , Knud Zabrocki , Michael Schulz

Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or…

Statistical Mechanics · Physics 2012-11-30 Matteo Smerlak

We complete the kinetic theory of inhomogeneous systems with long-range interactions initiated in previous works. We use a simpler and more physical formalism. We consider a system of particles submitted to a small external stochastic…

Statistical Mechanics · Physics 2023-08-23 Pierre-Henri Chavanis

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two indistinguishable fluids. The enhancement of the diffusive transport depends on the system size L and grows…

Mesoscale and Nanoscale Physics · Physics 2015-05-27 A. Donev , A. de la Fuente , J. B. Bell , A. L. Garcia

We study the formation and the evolution of velocity distribution tails for systems with long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a…

Statistical Mechanics · Physics 2009-11-11 Pierre-Henri Chavanis , Mohammed Lemou

Using the Feynman-Kac formula, a work fluctuation theorem for a Brownian particle in a nonconfining potential, e.g., a potential well with finite depth, is derived. The theorem yields aninequality that puts a lower bound on the average work…

Statistical Mechanics · Physics 2021-02-12 Christoph Streißnig , Holger Kantz

The temporal Fokker-Plank equation [{\it J. Stat. Phys.}, {\bf 3/4}, 527 (2003)] or propagation-dispersion equation was derived to describe diffusive processes with temporal dispersion rather than spatial dispersion as in classical…

Statistical Mechanics · Physics 2016-02-01 Jean Pierre Boon , James F. Lutsko

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 fluctuation-dissipation theorem is a central result in statistical mechanics and is usually formulated for systems described by diffusion processes. In this paper, we propose a generalization for a wider class of stochastic processes,…

Statistical Mechanics · Physics 2018-09-20 Alberto Montefusco , Mark A. Peletier , Hans Christian Öttinger

The reformulation of nonequilibirum thermodynamics, to include the treatment of thermodynamic fluctuations, is applied to the hydrodynamic fluctuations of a simple fluid. It is shown that the nonequilibrium thermodynamic scheme leads to the…

Statistical Mechanics · Physics 2007-05-23 J. M. Rubi , P. Mazur

A fully quantum treatment of Einstein's Brownian motion is given, showing in particular the role played by the two original requirements of translational invariance and connection between dynamics of the Brownian particle and atomic nature…

Quantum Physics · Physics 2007-05-23 Francesco Petruccione , Bassano Vacchini

Generalizations of Onsager reciprocity relations are established for the nonlinear response coefficients of ballistic transport in the effusion of gaseous mixtures. These generalizations, which have been established on the basis of the…

Statistical Mechanics · Physics 2011-03-29 Pierre Gaspard , David Andrieux

The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance.…

Statistical Mechanics · Physics 2015-05-30 Haidong Feng , Jin Wang