Power injected in a granular gas

TL;DR

This paper analytically determines the distribution of power injected into a steady-state granular gas under different thermostats, highlighting its importance for fluctuation relations in dissipative systems.

Contribution

It introduces an analytic method to compute the full distribution of injected power in a granular gas with stochastic or deterministic thermostats, advancing understanding of steady-state dissipation.

Findings

Derived the full distribution of injected power in a granular gas.

Compared stochastic and deterministic thermostat effects on power injection.

Discussed implications for fluctuation relations in dissipative systems.

Abstract

A granular gas may be modeled as a set of hard-spheres undergoing inelastic collisions; its microscopic dynamics is thus strongly irreversible. As pointed out in several experimental works bearing on turbulent flows or granular materials, the power injected in a dissipative system to sustain a steady-state over an asymptotically large time window is a central observable. We describe an analytic approach allowing us to determine the full distribution of the power injected in a granular gas within a steady-state resulting from subjecting each particle independently either to a random force (stochastic thermostat) or to a deterministic force proportional to its velocity (Gaussian thermostat). We provide an analysis of our results in the light of the relevance, for other types of systems, of the injected power to fluctuation relations.