  A system that violates detailed balance evolves asymptotically into a
nonequilibrium steady state with non-vanishing currents. Analogously, when
detailed balance holds at any instant of time but the system is driven through
time-periodic variations of external parameters, it evolves toward a
time-periodic state, which can also support non-vanishing currents. In both
cases the maintenance of currents throughout the system incurs a cost in terms
of entropy production. Here we compare these two scenarios for one dimensional
diffusive systems with periodic boundary condition, a framework commonly used
to model biological and artificial molecular machines. We first show that the
entropy production rate in a periodically driven system is necessarily greater
than that in a stationary system without detailed balance, when both are
described by the same (time-averaged) current and probability distribution.
Next, we show how to construct both a non-equilibrium steady state and a
periodic driving that support a given time averaged probability distribution
and current. Lastly, we show that although the entropy production rate of a
periodically driven system is higher than that of an equivalent steady state,
the difference between the two entropy production rates can be tuned to be
arbitrarily small.
