Thermodynamics of trajectories and local fluctuation theorems for harmonic quantum networks

TL;DR

This paper introduces a phase-space method for analyzing the thermodynamics and fluctuation theorems of quantum harmonic networks, enabling detailed study of quantum jump trajectories and exchange statistics.

Contribution

It provides a novel phase-space approach to analyze thermodynamics and fluctuation theorems in quantum harmonic networks with linear and bilinear dynamics.

Findings

Validates a local fluctuation theorem for excitation exchange.

Demonstrates the method on different coupling schemes.

Enables full counting statistics analysis of quantum trajectories.

Abstract

We present a general method to undertake a thorough analysis of the thermodynamics of the quantum jump trajectories followed by an arbitrary quantum harmonic network undergoing linear and bilinear dynamics. The approach is based on the phase-space representation of the state of a harmonic network. The large deviation function associated with this system encodes the full counting statistics of exchange and also allows one to deduce for fluctuation theorems obeyed by the dynamics. We illustrate the method showing the validity of a local fluctuation theorem about the exchange of excitations between a restricted part of the environment (i.e., a local bath) and a harmonic network coupled with different schemes.