Fluctuation of the entropy production for the Lorentz gas under small external forces

TL;DR

This paper investigates the entropy production fluctuations in a Lorentz gas model under small external forces, demonstrating that the entropy production obeys the Gallavotti-Cohen fluctuation relation using advanced mathematical tools.

Contribution

It establishes the fluctuation relation for entropy production in a driven Lorentz gas, extending previous models with new analytical techniques.

Findings

Entropy production satisfies the Gallavotti-Cohen fluctuation relation.

The study characterizes non-equilibrium steady states as SRB measures.

Uses anisotropic Banach spaces to analyze phase space contraction.

Abstract

In this paper we study the physical and statistical properties of the periodic Lorentz gas with finite horizon driven to a non-equilibrium steady state by the combination of non-conservative external forces and deterministic thermostats. A version of this model was introduced by Chernov, Eyink, Lebowitz, and Sinai and subsequently generalized by Chernov and the third author. Non-equilibrium steady states for these models are SRB measures and they are characterized by the positivity of the steady state entropy production rate. Our main result is to establish that the entropy production, in this context equal to the phase space contraction, satisfies the Gallavotti-Cohen fluctuation relation. The main tool needed in the proof is the family of anisotropic Banach spaces introduced by the first and third authors to study the ergodic and statistical properties of billiards using transfer operator techniques.