Mapping out of equilibrium into equilibrium in one-dimensional transport models

Simple item page
dc.creatorTailleur, Julien
dc.creatorKurchan, Jorge
dc.creatorLecomte, Vivien
dc.date2008-09-03
dc.date2008-11-13
dc.date.accessioned2026-07-07T10:17:37Z
dc.date.available2026-07-07T10:17:37Z
dc.descriptionSystems with conserved currents driven by reservoirs at the boundaries offer an opportunity for a general analytic study that is unparalleled in more general out of equilibrium systems. The evolution of coarse-grained variables is governed by stochastic {\em hydrodynamic} equations in the limit of small noise.} As such it is amenable to a treatment formally equal to the semiclassical limit of quantum mechanics, which reduces the problem of finding the full distribution functions to the solution of a set of Hamiltonian equations. It is in general not possible to solve such equations explicitly, but for an interesting set of problems (driven Symmetric Exclusion Process and Kipnis-Marchioro-Presutti model) it can be done by a sequence of remarkable changes of variables. We show that at the bottom of this `miracle' is the surprising fact that these models can be taken through a non-local transformation into isolated systems satisfying detailed balance, with probability distribution given by the Gibbs-Boltzmann measure. This procedure can in fact also be used to obtain an elegant solution of the much simpler problem of non-interacting particles diffusing in a one-dimensional potential, again using a transformation that maps the driven problem into an undriven one.
dc.identifierhttps://arxiv.org/abs/0809.0709
dc.identifierhttp://arxiv.org/abs/0809.0709
dc.identifierJ. Phys. A: Math. Theor. 41, 505001, (2008)
dc.identifierdoi:10.1088/1751-8113/41/50/505001
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/173911
dc.subjectStatistical Mechanics
dc.titleMapping out of equilibrium into equilibrium in one-dimensional transport models
dc.typetext

Files

Collections

arXiv