A quantum fluctuation theorem for any Lindblad master equation

TL;DR

This paper derives a comprehensive quantum fluctuation theorem applicable to open quantum systems with multiple environments, encompassing non-equilibrium and time-dependent scenarios, and extends to nonthermal baths and explicit system-bath interactions.

Contribution

It introduces a general quantum fluctuation theorem valid for various regimes and bath types, unifying and extending previous results like the Jarzynski equality.

Findings

The theorem applies to both local and global master equations.

It holds for time-dependent Hamiltonians and nonthermal baths.

The fluctuation theorem relates time-reversed dynamics to entropy correlations.

Abstract

We present a general quantum fluctuation theorem for the entropy production of an open quantum system coupled to multiple environments, not necessarily at equilibrium. Such a general theorem, when restricted to the weak-coupling and Markovian regime, holds for both local and global master equations, corroborating the thermodynamic consistency of local quantum master equations. The theorem is genuinely quantum, as it can be expressed in terms of conservation of a Hermitian operator, describing the dynamics of the system state operator and of the entropy change in the baths. The integral fluctuation theorem follows from the properties of such an operator. Furthermore, it is also valid when the system is described by a time-dependent Hamiltonian. As such, the quantum Jarzynski equality is a particular case of the general result presented here. Moreover, our result can be extended to nonthermal baths, as long as microreversibility is preserved. We present some numerical examples to showcase the exact results previously obtained. We finally generalize the fluctuation theorem to the case where the interaction between the system and the bath is explicitly taken into account. We show that the fluctuation theorem amounts to a relation between time-reversed dynamics of the global density matrix and a two-time correlation function along the forward dynamics involving the baths' entropy alone.