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Nonequilibrium thermodynamics of the Markovian Mpemba effect and its inverse

Significance It is commonly expected that cooling a hot system takes a longer time than cooling an identical system initiated at a lower temperature. Surprisingly, this is not always the case; in various systems, including water and magnetic alloys, it has been observed that a hot system can be cooled faster. These anomalous cooling effects are referred to as “the Mpemba effect”, and so far they lack a generic details-independent explanation. Based on recent developments in the theory of nonequilibrium thermodynamics, we propose a generic mechanism for similar effects, demonstrate it in various systems, and predict a similar anomalous behavior in heating. Under certain conditions, it takes a shorter time to cool a hot system than to cool the same system initiated at a lower temperature. This phenomenon—the “Mpemba effect”—was first observed in water and has recently been reported in other systems. Whereas several detail-dependent explanations were suggested for some of these observations, no common underlying mechanism is known. Using the theoretical framework of nonequilibrium thermodynamics, we present a widely applicable mechanism for a similar effect, the Markovian Mpemba effect, derive a sufficient condition for its appearance, and demonstrate it explicitly in three paradigmatic systems: the Ising model, diffusion dynamics, and a three-state system. In addition, we predict an inverse Markovian Mpemba effect in heating: Under proper conditions, a cold system can heat up faster than the same system initiated at a higher temperature. We numerically demonstrate that this inverse effect is expected in a 1D antiferromagnet nearest-neighbors interacting Ising chain in the presence of an external magnetic field. Our results shed light on the mechanism behind anomalous heating and cooling and suggest that it should be possible to observe these in a variety of systems.