Quantum fluctuation theorem: Can we go from micro to meso?

TL;DR

This paper explores the extension of the quantum fluctuation theorem from microscopic to mesoscopic systems, specifically using a Lindblad master equation, and establishes a rigorous connection between the two regimes.

Contribution

It provides a rigorous link between microscopic and mesoscopic quantum fluctuation theorems using a Lindblad model, addressing a practical gap in the field.

Findings

FT holds for the Lindblad master equation model.

The quantum FT is satisfied by the Lesovik-Levitov charge transport formula.

A rigorous connection between microscopic and mesoscopic FT is established.

Abstract

Quantum extensions of the Gallavotti-Cohen fluctuation theorem (FT) for the entropy production have been discussed by several authors. There is a practical gap between microscopic forms of FT and mesoscopic (i.e. not purely Hamiltonian) forms for open systems. In a microscopic setup, it is easy to state and to prove FT. In a mesoscopic setup, it is difficult to identify fluctuations of the entropy production. (This difficulty is absent in the classical case.) We discuss a particular mesoscopic model: a Lindblad master equation, in which we state FT and, more importantly, connect it rigorously with the underlying microscopic FT. We also remark that FT is satisfied by the Lesovik-Levitov formula for statistics of charge transport.