First, the kinetic or thermal route, in which the emergence of the Mpemba effect is marked by the crossing of the evolution curves of the kinetic temperature (average kinetic energy). The Mpemba effect is analyzed via two alternative routes, recently considered in the literature. In this paper, we investigate the Mpemba effect in a molecular gas with nonlinear drag, both analytically - by employing the tools of kinetic theory - and numerically - direct simulation Monte Carlo of the kinetic equation and event-driven molecular dynamics. Loosely speaking, the Mpemba effect appears when the hotter cools sooner or, in a more abstract way, when the further from equilibrium relaxes faster. Finally, theoretical results are compared with direct simulation Monte Carlo and molecular dynamics results, and a very good agreement is found. In order to obtain explicit results, we use a well-founded Maxwellian approximation for the evolution dynamics and the steady-state quantities. The election of parameters allows to design plausible protocols based on these thermostats for generating the initial states to observe the Mpemba-like effect in experiments. Later, an overshoot of the temperature evolution with respect to the steady-state value is observed and the mechanism of Mpemba effect generation is changed. Firstly, Mpemba effect is characterized by the appearance of a crossing between the temperature curves of the considered samples. We realize that a certain choice of a thermostat of this class can be characterized just by the total intensity and the fraction of noise transferred to the rotational degree of freedom with respect to the translational ones. Thus, granular particles are affected by a stochastic force and a stochastic torque, which inject translational and rotational energy, respectively.

We study the conditions under which a Mpemba-like effect emerges in granular gases of inelastic and rough hard disks driven by a class of thermostats characterized by the splitting of the noise intensity into translational and rotational counterparts.

Does hot water freeze faster