  Engineered swift equilibration (ESE) is a class of driving protocols that
enforce an equilibrium distribution with respect to external control parameters
at the beginning and end of rapid state transformations of open, classical
non-equilibrium systems. ESE protocols have previously been derived and
experimentally realized for Brownian particles in simple, one-dimensional,
time-varying trapping potentials; one recent study considered ESE in
two-dimensional Euclidean configuration space. Here we extend the ESE framework
to generic, overdamped Brownian systems in arbitrary curved configuration space
and illustrate our results with specific examples not amenable to previous
techniques. Our approach may be used to impose the necessary dynamics to
control the full temporal configurational distribution in a wide variety of
experimentally realizable settings.
