Microcanonical quantum fluctuation theorems

TL;DR

This paper generalizes quantum fluctuation theorems for work to include arbitrary initial states and degenerate Hamiltonians, deriving explicit formulas and a new entropy-from-work relation that can be experimentally tested.

Contribution

It introduces generalized fluctuation theorems for microcanonical states and links work distributions to entropy measurements without requiring time reversal.

Findings

Explicit formulas for work characteristic function in microcanonical states

Derivation of a Crooks-type fluctuation theorem for microcanonical systems

Proposed entropy-from-work relation for experimental entropy measurement

Abstract

Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the respective canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians.From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.