  The Mpemba effect denotes an anomalous relaxation phenomenon where a system
initially at a hot temperature cools faster than a system that starts at a less
elevated temperature. We introduce an isothermal analog of this effect for a
system prepared in a non-equilibrium steady state that then relaxes towards
equilibrium. Here, the driving strength, which determines the initial
non-equilibrium steady state, takes the role of the temperature in the original
version. As a paradigm, we consider a particle initially driven by a
non-conservative force along a one-dimensional periodic potential. We show that
for an asymmetric potential relaxation from a strongly driven initial state is
faster than from a more weakly driven one at least for one of the two possible
directions of driving. These results are first obtained through perturbation
theory in the strength of the potential and then extended to potentials of
arbitrary strength through topological arguments.
