Mpemba Effect in Anisotropically Driven Inelastic Maxwell Gases

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 Maxwell 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.