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

TL;DR

This paper links the Mpemba effect, where hot systems cool faster than warm ones, to a non-monotonic temperature dependence of extractable work in metastable systems, supported by experimental and theoretical analysis.

Contribution

It demonstrates that the metastable Mpemba effect is due to a non-monotonic relationship between initial temperature and maximum extractable work in a double-well potential system.

Findings

Experimental observation of the Mpemba effect in colloidal particles.

Identification of non-monotonic temperature dependence of extractable work.

Theoretical explanation linking the effect to local equilibrium dynamics.

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.