Kinetic approach to the Gaussian thermostat in a dilute sheared gas in the thermodynamic limit

TL;DR

This paper investigates the behavior of a dilute sheared gas under a Gaussian thermostat, showing that in the thermodynamic limit the thermostat acts as a friction force, while finite systems exhibit Gaussian fluctuations that challenge fluctuation-dissipation relations.

Contribution

It provides a kinetic analysis of the Gaussian thermostat's role in a sheared gas, revealing its limiting behavior and fluctuation characteristics for finite systems.

Findings

Thermostat acts as a constant friction force in the thermodynamic limit.

Finite systems exhibit Gaussian fluctuations with deviations for large fluctuations.

Fluctuation-dissipation relations are invalid far from equilibrium due to these fluctuations.

Abstract

A dilute gas of particles with short range interactions is considered in a shearing stationary state. A Gaussian thermostat keeps the total kinetic energy constant. For infinitely many particles it is shown that the thermostat becomes a friction force with constant friction coefficient. For finite number of particles N, the fluctuations around this constant are of order one over the square root of N, and distributed approximately Gaussian with deviations for large fluctuations. These deviations prohibit a derivation of fluctuation-dissipation relations far from equilibrium, based on the Fluctuation Theorem.