Mpemba effect in anisotropically driven inelastic Maxwell gases

TL;DR

This paper demonstrates the existence of the Mpemba effect in anisotropically driven inelastic Maxwell gases, showing that hotter systems can relax faster than cooler ones even from steady states, with exact conditions derived.

Contribution

It provides the first exact analysis of the Mpemba effect in anisotropically driven granular gases, extending previous isotropic studies to steady initial states.

Findings

Mpemba effect exists in anisotropically driven granular gases.

Conditions for the effect and its inverse are explicitly derived.

Hotter systems can cool exponentially faster under certain conditions.

Abstract

Through an exact analysis, we show the existence of Mpemba effect in an anisotropically driven inelastic Maxwell gas, a simplified model for granular gases, in two dimensions. Mpemba effect refers to the couterintuitive phenomenon of a hotter system relaxing to the steady state faster than a cooler system, when both are quenched to the same lower temperature. The Mpemba effect has been illustrated in earlier studies on isotropically driven granular gases, but its existence requires non-stationary initial states, limiting experimental realisation. In this paper, we demonstrate the existence of the Mpemba effect in anisotropically driven granular gases even when the initial states are non-equilibrium steady states. The precise conditions for the Mpemba effect, its inverse, and the stronger version, where the hotter system cools exponentially faster are derived.