Linear response in the uniformly heated granular gas

TL;DR

This paper studies the linear response of a uniformly heated granular gas, analyzing relaxation after small perturbations and a Kovacs-like protocol, revealing conditions for anomalous responses and confirming results with simulations.

Contribution

It introduces a detailed analysis of the linear response and Kovacs effect in granular gases, including new fluctuation-dissipation relations and identification of conditions for anomalous behavior.

Findings

Good agreement between analytical results and numerical simulations.

Identification of a critical inelasticity value for anomalous Kovacs response.

Derivation of generalized fluctuation-dissipation relations for the system.

Abstract

We analyse the linear response properties of the uniformly heated granular gas. The intensity of the stochastic driving fixes the value of the granular temperature in the non-equilibrium steady state reached by the system. Here, we investigate two specific situations. First, we look into the ``direct'' relaxation of the system after a single (small) jump of the driving intensity. This study is carried out by two different methods. Not only do we linearise the evolution equations around the steady state, but also derive generalised out-of-equilibrium fluctuation-dissipation relations for the relevant response functions. Second, we investigate the behaviour of the system in a more complex experiment, specifically a Kovacs-like protocol with two jumps in the driving. The emergence of anomalous Kovacs response is explained in terms of the properties of the direct relaxation function: it is the second mode changing sign at the critical value of the inelasticity that demarcates anomalous from normal behaviour. The analytical results are compared with numerical simulations of the kinetic equation, and a good agreement is found.