  We establish a correspondence between two very general paradigms for systems
that persist away from thermal equilibrium. In the first paradigm, a
nonequilibrium steady state (NESS) is maintained by applying fixed
thermodynamic forces that break detailed balance. In the second paradigm, known
as a stochastic pump (SP), a time-periodic state is maintained by the periodic
variation of a system's external parameters. In both cases, currents are
generated and entropy is produced. Restricting ourselves to discrete-state
systems, we establish a mapping between these scenarios. Given a NESS
characterized by a particular set of stationary probabilities, currents and
entropy production rates, we show how to construct a SP with exactly the same
(time-averaged) values. The mapping works in the opposite direction as well.
These results establish an equivalence between the two paradigms, by showing
that stochastic pumps are able to mimic the behavior of nonequilibrium steady
states, and vice-versa.
