Stochastic thermodynamics of rapidly driven systems

TL;DR

This paper develops a stochastic thermodynamics framework for open quantum systems under rapid external driving, deriving fundamental thermodynamic relations and fluctuation theorems without the need for time-reversed driving, and illustrates these on a thermodynamic engine model.

Contribution

It introduces a modified stochastic master equation in the Floquet basis for rapidly driven quantum systems, establishing thermodynamic laws and fluctuation theorems without time-reversal of external driving.

Findings

Derived a steady-state fluctuation theorem for currents and work rate.

Showed that the two-step energy measurement becomes unnecessary in the long-time limit.

Demonstrated the framework on a quantum thermodynamic engine model.

Abstract

We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the Floquet basis. Transition rates are shown to satisfy the local detailed balance involving the entropy flowing out of the reservoirs. The first and second law of thermodynamics are also identified at the trajectory level. Mechanical work is identified by means of initial and final projections on energy eigenstates of the system. We explicitly show that this two step measurement becomes unnecessary in the long time limit. A steady-state fluctuation theorem for the currents and rate of mechanical work is also established. This relation does not require the introduction of a time reversed external driving which is usually needed when considering systems subjected to time asymmetric external fields. This is understood as a consequence of the secular approximation applied in consistency with the large time scale separation between the fast driving oscillations and the slower relaxation dynamics induced by the environment. Our results are finally illustrated on a model describing a thermodynamic engine.