On the Quantum Jarzynski Identity

TL;DR

This paper presents a compact formulation and proof of the quantum Jarzynski identity for open systems, emphasizing heat flow measurement over direct work measurement using Hermitian map superoperators.

Contribution

It introduces a novel approach to express and prove the quantum Jarzynski identity without direct work measurement, utilizing Hermitian maps for heat flow representation.

Findings

Provides a new proof of the quantum Jarzynski identity for open systems

Introduces Hermitian map superoperators for heat flow measurement

Avoids explicit work measurement by focusing on environmental heat flow

Abstract

In this note, we will discuss how to compactly express and prove the Jarzynski identity for an open quantum system with dissipative dynamics. We will avoid explicitly measuring the work directly, which is tantamount to continuously monitoring the system, and instead measure the heat flow from the environment. We represent the measurement of heat flow with Hermitian map superoperators that act on the system density matrix. Hermitian maps provide a convenient and compact representation of sequential measurement and correlation functions.