  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.
