# Mapping out of equilibrium into equilibrium in one-dimensional transport models - Condensed Matter > Statistical Mechanics

Mapping out of equilibrium into equilibrium in one-dimensional transport models - Condensed Matter > Statistical Mechanics - Download this document for free, or read online. Document in PDF available to download.

Abstract: Systems with conserved currents driven by reservoirs at the boundaries offeran opportunity for a general analytic study that is unparalleled in moregeneral out of equilibrium systems. The evolution of coarse-grained variablesis governed by stochastic {\em hydrodynamic} equations in the limit of smallnoise.} As such it is amenable to a treatment formally equal to thesemiclassical limit of quantum mechanics, which reduces the problem of findingthe full distribution functions to the solution of a set of Hamiltonianequations. It is in general not possible to solve such equations explicitly,but for an interesting set of problems driven Symmetric Exclusion Process andKipnis-Marchioro-Presutti model it can be done by a sequence of remarkablechanges of variables. We show that at the bottom of this `miracle- is thesurprising fact that these models can be taken through a non-localtransformation into isolated systems satisfying detailed balance, withprobability distribution given by the Gibbs-Boltzmann measure. This procedurecan in fact also be used to obtain an elegant solution of the much simplerproblem of non-interacting particles diffusing in a one-dimensional potential,again using a transformation that maps the driven problem into an undriven one.

Author: Julien Tailleur, Jorge Kurchan, Vivien Lecomte

Source: https://arxiv.org/