Temperature probes in binary granular gases

TL;DR

This study examines the validity of Fluctuation-Dissipation relations in binary granular gases with different properties, revealing that each component obeys its own FD relation and that a single-particle thermometer measures its own temperature rather than the surrounding medium.

Contribution

It demonstrates that classical Green-Kubo relations hold separately for each component in granular mixtures, even when energy equipartition is broken, and explores the behavior of a single-particle thermometer.

Findings

FD relations hold for each component individually

Granular temperatures differ between components

Single-particle thermometer measures its own temperature

Abstract

We investigate the validity of Fluctuation-Dissipation (FD) relations for a mixture of two granular gases with different physical properties (restitution coefficients or masses) subject to stochastic driving. It is well known that the partial granular temperatures T_1 and T_2 of the two components are different, i.e. energy equipartition is broken. We observe, with numerical simulations of inelastic hard disks in homogeneous and non-homogeneous situations, that the classical equilibrium Green-Kubo relations are satisfied separately for each component of the gas, the role of the equilibrium temperature being played by the granular temperature of each component. Of particular interest is the limit in which one of the two components consists of only one particle, representing a non-perturbing thermometer. In this case it turns out that such a thermometer is measuring its own temperature and not that of the surrounding granular media, which in general will be different.