Operational work fluctuation theorem for open quantum systems

TL;DR

This paper introduces a quantum fluctuation theorem applicable to open quantum systems that provides bounds on free energy differences based on measurable work, overcoming limitations of previous TPM-based approaches.

Contribution

It proposes a new quantum fluctuation theorem valid for open systems that does not require detailed knowledge of the system Hamiltonian, unlike prior TPM-based methods.

Findings

The theorem applies to open quantum systems and is experimentally measurable.

It provides bounds on free energy differences rather than exact values.

The inequality becomes an equality in the classical limit with no energy coherences.

Abstract

The classical Jarzynski equality establishes an exact relation between the stochastic work performed on a system driven out of thermal equilibrium and the free energy difference in a corresponding quasi-static process. This fluctuation theorem bears experimental relevance, as it enables the determination of the free energy difference through the measurement of externally applied work in a nonequilibrium process. In the quantum case, the Jarzynski equality only holds if the measurement procedure of the stochastic work is drastically changed: it is replaced by a so-called two-point measurement (TPM) scheme that requires the knowledge of the initial and final Hamiltonian and therefore lacks the predictive power for the free energy difference that the classical Jarzynski equation is known for. Here, we propose a quantum fluctuation theorem that is valid for externally measurable quantum work determined during the driving protocol. In contrast to the TPM case, the theorem also applies to open quantum systems and the scenario can be realized without knowing the system Hamiltonian. Our fluctuation theorem comes in the form of an inequality and therefore only yields bounds to the true free energy difference. The inequality is saturated in the quasiclassical case of vanishing energy coherences at the beginning and at the end of the protocol. Thus, there is a clear quantum disadvantage.