  Mpemba effect refers to the counterintuitive result that, when quenched to a
low temperature, a system at higher temperature may equilibrate faster than one
at intermediate temperatures. This effect has recently been demonstrated in
driven granular gases, both for smooth as well as rough hard-sphere systems
based on a perturbative analysis. In this paper, we consider the inelastic
driven Maxwell gas, a simplified model for a granular gas, where the rate of
collision is assumed to be independent of the relative velocity. Through an
exact analysis, we determine the conditions under which a Mpemba effect is
present in this model. For mono-dispersed gases, we show that the Mpemba effect
is present only when the initial states are allowed to be non-stationary, while
for bi-dispersed gases, it is present for steady state initial states. We also
demonstrate the existence of the strong Mpemba effect for bi-dispersed Maxwell
gas wherein the system at higher temperature relaxes to a final steady state at
an exponentially faster rate leading to smaller equilibration time.

Statistical Mechanics