The principle of microreversibility and the fluctuation relations for quantum systems driven out of equilibrium

TL;DR

This paper extends classical fluctuation relations to quantum systems, deriving new quantum Crooks and Jarzynski relations that connect nonequilibrium work and response theory without relying solely on microreversibility.

Contribution

It introduces quantum extensions of Crooks-Jarzynski and Crooks relations, linking nonequilibrium work relations with linear response theory in quantum systems.

Findings

Derived quantum Crooks-Jarzynski relation without microreversibility.

Established quantum Crooks relation leading to Jarzynski equality.

Connected fluctuation theorems with linear response in quantum systems.

Abstract

For classical systems driven out of equilibrium, Crooks derived a relation (the Crooks-Jarzynski relation), whose special cases include a relation (the Crooks relation) equivalent to the Kawasaki non-linear response relation. We derive a quantum extension of the Crooks-Jarzynski relation without explicitly using the principle of microreversibility. Its special cases lead to the Jarzynski equality and the standard linear response theory with a Green-Kubo formula with a canonical correlation function. We also derive a quantum extension of the Crooks relation using the principle of microreversibility. Its special cases lead to the Jarzynski equality, the Crooks transient fluctuation theorem, and the fluctuation theorem for current or shear stress, which leads to a Green-Kubo formula with a symmetrized correlation function. For each quantum Crooks relation, there exists a corresponding quantum Crooks-Jarzynski relation. Using either relation, we can derive the Jarzynski equality, the fluctuation theorems mentioned above, and the standard linear response theory.