  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.
