  Periodic driving is used to operate machines that go from standard
macroscopic engines to small non-equilibrium micro-sized systems. Two classes
of such systems are small heat engines driven by periodic temperature
variations and molecular pumps driven by external stimuli. Well known results
that are valid for nonequilibrium steady states of systems driven by fixed
thermodynamic forces, instead of an external periodic driving, have been
generalized to periodically driven heat engines only recently. These results
include a general expression for entropy production in terms of currents and
affinities and symmetry relations for the Onsager coefficients from linear
response theory. For nonequilibrium steady states, the Onsager reciprocity
relations can be obtained from the more general fluctuation theorem for the
currents. We prove a fluctuation theorem for the currents for periodically
driven systems. We show that this fluctuation theorem implies a fluctuation
dissipation relation, symmetry relations for Onsager coefficients and further
relations for nonlinear response coefficients. The setup in this paper is more
general than previous studies, i.e., our results are valid for both heat
engines and molecular pumps. The external protocol is assumed to be stochastic
in our framework, which leads to a particularly convenient way to treat
periodically driven systems.
