Non-equilibrium fluctuations in a driven stochastic Lorentz gas

TL;DR

This paper investigates the non-equilibrium fluctuations of a driven stochastic Lorentz gas, analyzing entropy production and work fluctuations, revealing conditions under which fluctuation relations hold or break down.

Contribution

It provides a detailed analysis of entropy production and work fluctuations in a driven Lorentz gas, highlighting the regimes where fluctuation relations are valid or violated.

Findings

At small external fields, entropy production and work distributions collapse and satisfy the Fluctuation Relation.

At large external fields, work fluctuations violate the Fluctuation Relation, while entropy production still satisfies it.

The study clarifies the behavior of non-equilibrium fluctuations in a kinetic model with elastic and inelastic collisions.

Abstract

We study the stationary state of a one-dimensional kinetic model where a probe particle is driven by an external field E and collides, elastically or inelastically, with a bath of particles at temperature T. We focus on the stationary distribution of the velocity of the particle, and of two estimates of the total entropy production \Delta s_tot. One is the entropy production of the medium \Delta s_m, which is equal to the energy exchanged with the scatterers, divided by a parameter \theta, coinciding with the particle temperature at E=0. The other is the work W done by the external field, again rescaled by \theta. At small E, a good collapse of the two distributions is found: in this case the two quantities also verify the Fluctuation Relation (FR), indicating that both are good approximations of \Delta s_tot. Differently, for large values of E, the fluctuations of W violate the FR, while \Delta s_m still verifies it.