Inference of entropy production for periodically driven systems

The problem of estimating entropy production from incomplete information in stochastic thermodynamics is essential for theory and experiments. Whereas a considerable amount of work has been done on this topic, arguably, most of it is restricted to the case of nonequilibrium steady states driven by a fixed thermodynamic force. Based on a recent method that has been proposed for nonequilibrium steady states, we obtain an estimate of the entropy production based on the statistics of visible transitions and their waiting times for the case of periodically driven systems. The time-dependence of transition rates in periodically driven systems produces several differences in relation to steady states, which is reflected in the entropy production estimation. More specifically, we propose an estimate that does depend on the time between transitions but is independent of the specific time of the first transition, thus it does not require tracking the protocol. Formally, this elimination of the time-dependence of the first transition leads to an extra term in the inequality that involves the rate of entropy production and its estimate. We analyze a simple model of a molecular pump to understand the relation between the performance of the method and physical quantities such as energies, energy barriers, and thermodynamic affinity. Our results with this model indicate that the emergence of net motion in the form of a probability current in the space of states is a necessary condition for a relevant estimate of the rate of entropy production.