Mpemba effect in a sheared granular gas with velocity-dependent restitution

TL;DR

This paper demonstrates the Mpemba effect in a sheared granular gas with velocity-dependent restitution, showing faster relaxation of higher initial temperatures and multiple crossings in temperature and viscosity relaxation curves.

Contribution

It introduces a kinetic mechanism explaining multiple Mpemba effects in driven granular gases with velocity-dependent restitution.

Findings

Higher initial temperature systems can relax faster than lower ones.

Multiple crossings in temperature and viscosity relaxation curves are observed.

Velocity dependence of restitution introduces an intrinsic timescale leading to multiple Mpemba effects.

Abstract

We investigate the Mpemba effect in a dilute sheared granular gas with a velocity-dependent restitution coefficient. Using kinetic theory based on Grad's moment method, we analyze the relaxation dynamics following a sudden change in the shear rate. We show that, despite having a higher initial temperature, a system starting from an isotropic state can relax faster than a system prepared in a sheared steady state, demonstrating a clear Mpemba effect in the temperature evolution. We further demonstrate the emergence of a viscosity Mpemba effect, characterized by crossings in the relaxation curves of the shear viscosity. Remarkably, multiple crossings arise due to an additional intrinsic timescale introduced by the velocity dependence of the restitution coefficient, providing a minimal kinetic mechanism for multiple Mpemba effects in driven granular gases.