Mpemba effect protocol for inelastic and rough granular gases*

We study the conditions under which the Mpemba effect emerges in inelastic and rough granular gases driven by a class of thermostats characterized by the splitting of the noise intensity into translational and rotational counterparts. Thus, granular particles are affected by a stochastic force and a stochastic torque, which inject translational and rotational energy respectively. We realize that only the total intensity and the fraction of noise transferred to rotational degrees of freedom with respect to the translational ones are the quantities must be adjusted to have one certain thermostat of this class. In order to obtain explicit results we use a well-founded Maxwellian approximation for the steady state quantities. Finally, from the achieved results we discuss a plausible protocol for observing Mpemba effect based on these thermostats.