The metastable Mpemba effect corresponds to a non-monotonic temperature dependence of extractable work

Abstract

The Mpemba effect refers to systems whose thermal relaxation time is a non-monotonic function of the initial temperature. Thus, a system that is initially hot cools to a bath temperature more quickly than the same system, initially warm. In the special case where the system dynamics can be described by a double-well potential with metastable and stable states, dynamics occurs in two stages: a fast relaxation to local equilibrium followed by a slow equilibration of populations in each coarse-grained state. We have recently observed the Mpemba effect experimentally in such a setting, for a colloidal particle immersed in water. Here, we show that this metastable Mpemba effect arises from a non-monotonic temperature dependence of the maximum amount of work that can be extracted from the local-equilibrium state at the end of Stage 1.

8 pages, 3 figures

References in corpus (2)

• Exponentially faster cooling in a colloidal system
• Overtaking while approaching equilibrium

Cited by in corpus (5)

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• The Mpemba effect in the Descartes protocol: A time-delayed Newton's law of cooling approach
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• Inducing and optimizing Markovian Mpemba effect with stochastic reset
• Thermal versus entropic Mpemba effect in molecular gases with nonlinear drag