Integral fluctuation theorems and trace-preserving map

TL;DR

This paper introduces a novel approach to integral fluctuation theorems using trace-preserving maps, simplifying the analysis of entropy production and heat exchange in quantum systems.

Contribution

It reformulates fluctuation theorems through constructed completely positive maps, connecting them to trace-preserving properties and Petz recovery maps.

Findings

Reformulation of integral fluctuation theorem via trace-preserving maps

Application to eigenstate fluctuation theorem and heat exchange

Natural emergence of Petz recovery map in the framework

Abstract

The detailed fluctuation theorem implies symmetry in the generating function of entropy production probability. The integral fluctuation theorem directly follows from this symmetry and the normalization of the probability. In this paper, we rewrite the generating function by integrating measurements and evolution into a constructed mapping. This mapping is completely positive, and the original integral FT is determined by the trace-preserving property of these constructed maps. We illustrate the convenience of this method by discussing the eigenstate fluctuation theorem and heat exchange between two baths. This set of methods is also applicable to the generating functions of quasi-probability, where we observe the Petz recovery map arising naturally from this approach.