Full counting statistics and fluctuation-dissipation relation for periodically driven two-state systems

Abstract

We derive the fluctuation theorem for a stochastic and periodically driven system coupled to two reservoirs with the aid of a master equation. We write down the cumulant generating functions for both the current and entropy production in closed compact forms so as to treat the adiabatic and nonadiabatic contributions systematically. We derive the fluctuation theorem by taking into account the time reversal symmetry and the property that the instantaneous currents flowing into the left and the right reservoir are not equal. It is found that the fluctuation-dissipation relation derived from the fluctuation theorem involves an expansion with respect to the time derivative of the affinity.

arXiv comment22 pages, 7 figures, revised for publication

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• Speed limits of the trace distance for open quantum system
• Controlling thermodynamics of a quantum heat engine with modulated amplitude drivings
• Asymptotic expansion of the solution of the master equation and its application to the speed limit
• Dynamical invariant formalism of shortcuts to adiabaticity
• Analysis of entropy production in finitely slow processes between nonequilibrium steady states
• Dynamical Lee-Yang zeros for continuous-time and discrete-time stochastic processes
• Demon driven by geometric phase
• Pumping current in a non-Markovian $N$-state model