Quantum work relations and response theory

TL;DR

This paper proves a universal quantum work relation for isolated systems in magnetic fields, deriving key results like the Jarzynski equality and Green-Kubo formula from microreversibility principles.

Contribution

It introduces a new quantum work relation applicable to time-dependent Hamiltonians in magnetic fields, unifying several fundamental response relations.

Findings

Derivation of a quantum work relation from microreversibility

Recovery of the quantum Jarzynski equality as a special case

Deduction of Green-Kubo and Casimir-Onsager relations

Abstract

A universal quantum work relation is proved for isolated time-dependent Hamiltonian systems in a magnetic field as the consequence of microreversibility. This relation involves a functional of an arbitrary observable. The quantum Jarzynski equality is recovered in the case this observable vanishes. The Green-Kubo formula and the Casimir-Onsager reciprocity relations are deduced thereof in the linear response regime.