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arXiv · 2004.11559

Mpemba effect in driven granular Maxwell gases

Apurba Biswas·V . V. Prasad·O. Raz·R. Rajesh
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Abstract

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.

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Apurba Biswas, V . V. Prasad, O. Raz, R. Rajesh. 2020-04-24. Mpemba effect in driven granular Maxwell gases. https://doi.org/10.1103/physreve.102.012906

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