Characteristic Functions Based on Quantum Jump Trajectory

TL;DR

This paper demonstrates a simple, trajectory-based method to derive characteristic functions for quantum thermodynamic quantities in quantum master equations, aligning with first-principles results and enabling experimental verification.

Contribution

It introduces a trajectory-based approach to derive characteristic functions in quantum thermodynamics, simplifying calculations and ensuring consistency with traditional methods.

Findings

Trajectory-based CF equations match first-principles results

Method facilitates experimental verification of quantum fluctuation relations

Simplifies the derivation of thermodynamic quantities in QMEs

Abstract

Characteristic functions (CFs) provide a very efficient method for evaluating the probability density functions of stochastic thermodynamic quantities and investigating their statistical features in quantum master equations (QMEs). A conventional procedure for obtaining these functions is to resort to a first-principles approach; namely, the evolution equations of the CFs of the combined system and its environment are obtained and then projected into the degrees of freedom of the system. However, the QMEs can be unraveled by a quantum jump trajectory. Thermodynamic quantities such as the heat, work, and entropy production can be well defined along a trajectory. Hence, on the basis of the notion of a trajectory, can we straightforwardly derive these CFs, e.g., their evolution equations? This is essential to establish the self-contained stochastic thermodynamics of a QME. In this paper, we show that it is indeed plausible and also simple. Particularly, these equations are fully consistent with those obtained by the first-principles method. Our results have practical significance; they indicate that the quantum fluctuation relations could be verified by more realistic photocounting experiments.