Quantum Extension of the Jarzynski Relation

TL;DR

This paper generalizes the classical Jarzynski relation to quantum systems, establishing a connection between work distribution and free energy differences in quantum regimes, applicable to isolated and open systems.

Contribution

It introduces a quantum extension of the Jarzynski relation using the adiabatic representation, applicable to both isolated and bath-coupled quantum systems.

Findings

The relation holds for isolated quantum systems.

The relation applies to systems coupled to a bath via a master equation.

A formal analogy with phase fluctuations in spectral lineshapes is established.

Abstract

The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary timescale, and the corresponding equilibrium free energy difference, is generalized to quantum systems. Using the adiabatic representation we show that this relation holds for isolated systems as well as for systems coupled to a bath described by a master equation. A close formal analogy is established between the present classical trajectory picture over populations of adiabatic states and phase fluctuations (dephasing) of a quantum coherence in spectral lineshapes, described by the stochastic Liouville equation.