(Global and Local) Fluctuations of Phase Space Contraction in Deterministic Stationary Non-equilibrium

Abstract

We studied numerically the validity of the fluctuation theorem, introduced by Evans,Cohen and Morris and proved by Gallavotti and Cohen, for a 2-dimensional system of particles maintained in a steady shear flow by Maxwell daemon boundary conditions (see Chernov and Lebowitz). The theorem was found to hold if one considers the total phase space contraction $σ$ occuring at collisions with both walls: $σ=σ^\su+σ^\giu$. An attempt to extend it to more local quantities $σ^\su$ and $σ^\giu$, corresponding to the collisions with the top or bottom wall only, gave negative results. The time decay of the correlations in $σ^{\su,\giu}$ was very slow compared to that of $σ$.