  For periodically driven systems, we derive a family of inequalities that
relate entropy production with experimentally accessible data for the mean, its
dependence on driving frequency, and the variance of a large class of
observables. With one of these relations, overall entropy production can be
bounded by just observing the time spent in a set of states. Among further
consequences, the thermodynamic efficiency both of isothermal cyclic engines
like molecular motors under a periodic load and of cyclic heat engines can be
bounded using experimental data without requiring knowledge of the specific
interactions within the system. We illustrate these results for a driven
three-level system and for a colloidal Stirling engine.
