Straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and the Jarzynski equality

TL;DR

This paper provides a straightforward quantum-mechanical derivation of the Crooks fluctuation theorem and Jarzynski equality for finite systems, emphasizing time-reversal symmetry and energy conservation without classical assumptions.

Contribution

It offers a novel, direct quantum approach to derive fundamental non-equilibrium fluctuation relations without relying on classical stochastic models.

Findings

Derivation applicable to isolated or weakly coupled systems

No need for master equations or classical phase-space assumptions

Highlights the fundamental role of time-reversal symmetry

Abstract

We obtain the Crooks and the Jarzynski non-equilibrium fluctuation relations using a direct quantum-mechanical approach for a finite system that is either isolated or coupled not too strongly to a heat bath. These results were hitherto derived mostly in the classical limit. The two main ingredients in the picture are the time-reversal symmetry and the application of the first law to the case where an agent performs work on the system. No further assumptions regarding stochastic or Markovian behavior are necessary, neither a master equation or a classical phase-space picture are required. The simplicity and the generality of these non-equilibrium relations are demonstrated, giving very simple insights into the Physics.