The Mpemba effect in granular fluids as a thermal memory effect

The Mpemba effect has been described in several systems, such as a water, spin glasses, granular gases and Markov chains. Originally, the Mpemba effect consists in an abnormally faster cooling process towards a stationary temperature for a system, as compared to an initially colder but otherwise identical system.

Our analysis is performed in the context of memory effecs in granular fluids. We proceed by solving the pertinent time evolution equations of the relevant moments of the particle distribution function. Additionally, we carry out computer simulations (molecular dynamics and Direct Simulation Monte Carlo simulation method). All three independent methods lead to the same behavior of thermal memory.

Our results reveal a rich variety of thermal memory effects, including the Mpemba effect. Moreover, we show that the type of thermal memory effect that eventually appears is selected according to the properties of the initial velocity distribution function.

In summary, we discuss the relevance of a the Mpemba effect within the more general landscape of memory effects in matter