Statistics of work and fluctuation theorems for microcanonical initial states

TL;DR

This paper investigates the statistical properties of work in quantum systems starting from a microcanonical state, deriving fluctuation theorems and validating the microcanonical Jarzynski equality through examples.

Contribution

It derives microcanonical fluctuation theorems and confirms the microcanonical Jarzynski equality for quantum systems undergoing parameter changes.

Findings

Transition probabilities obey detailed balance-like relations.

Microcanonical Jarzynski equality holds for sudden deformations.

Validation through examples with harmonic oscillator potential.

Abstract

The work performed on a system in a microcanonical state by changes in a control parameter is characterized in terms of its statistics. The transition probabilities between eigenstates of the system Hamiltonians at the beginning and the end of the parameter change obey a detailed balance-like relation from which various forms of the microcanonical fluctuation theorem are obtained. As an example, sudden deformations of a two dimensional harmonic oscillator potential are considered and the validity of the microcanonical Jarzynski equality connecting the degrees of degeneracy of energy eigenvalues before and after the control parameter change is confirmed.