Linear response in the uniformly heated granular gas

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.

arXiv comment14 pages, 10 figures; major revision; completely new section on non-equilibrium FDR; accepted for publication in PRE

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• Non-equilibrium memory effects: granular fluids and beyond
• Memory in Non-Monotonic Stress Response of an Athermal Disordered Solid
• Optimal control of uniformly heated granular fluids in linear response
• Time-delayed Newton's law of cooling with a finite-rate thermal quench: Impact on the Mpemba and Kovacs effects
• Kinetic glass transition in granular gases and non-linear molecular fluids