Generalized entropy production fluctuation theorems for quantum systems

TL;DR

This paper derives generalized quantum entropy production fluctuation theorems incorporating measurement and feedback effects, applicable to isolated, weakly coupled, and reservoir-contact quantum systems, extending classical results to quantum regimes.

Contribution

It introduces a unified framework for quantum entropy fluctuation theorems that include measurement and feedback, applicable across different system-environment interactions.

Findings

Fluctuation theorems retain classical form in quantum systems.

Second law inequality is modified by information in quantum context.

Results are robust against various measurement types.

Abstract

Based on trajectory dependent path probability formalism in state space, we derive generalized entropy production fluctuation relations for a quantum system in the presence of measurement and feedback. We have obtained these results for three different cases: (i) the system is evolving in isolation from its surroundings; (ii) the system being weakly coupled to a heat bath; and (iii) system in contact with reservoir using quantum Crooks fluctuation theorem. In case (iii), we build on the treatment carried out in [H. T. Quan and H. Dong, arxiv/cond-mat: 0812.4955], where a quantum trajectory has been defined as a sequence of alternating work and heat steps. The obtained entropy production fluctuation theorems retain the same form as in the classical case. The inequality of second law of thermodynamics gets modified in the presence of information. These fluctuation theorems are robust against intermediate measurements of any observable performed with respect to von Neumann projective measurements as well as weak or positive operator valued measurements.