Time-reversal symmetric work distributions for closed quantum dynamics in the histories framework

TL;DR

This paper introduces a new quantum work distribution based on the histories framework that respects thermodynamic principles and time-reversal symmetry, revealing non-classical features in quantum thermodynamics.

Contribution

It develops an alternative quantum work distribution for closed systems using the histories framework, overcoming limitations of the two-point measurement scheme.

Findings

The new distribution satisfies the first law of thermodynamics.

It maintains time-reversal symmetry in closed quantum dynamics.

The distribution can be negative and deviates from classical Jarzynski equality.

Abstract

A central topic in the emerging field of quantum thermodynamics is the definition of thermodynamic work in the quantum regime. One widely used solution is to define work for a closed system undergoing non-equilibrium dynamics according to the two-point energy measurement scheme. However, due to the invasive nature of measurement the two-point quantum work probability distribution leads to inconsistencies with two pillars of thermodynamics: it breaks the first law and the time-reversal symmetry expected for closed dynamics. We here introduce the quantum histories framework as a method to characterise the thermodynamic properties of the unmeasured, closed dynamics. Extending the classical phase space trajectories to continuous power operator trajectories allows us to derive an alternative quantum work distribution for closed quantum dynamics that fulfils the first law and is time-reversal symmetric. We find that the work distribution of the unmeasured dynamics leads to deviations from the classical Jarzynski equality and can have negative values highlighting distinctly non-classical features of quantum work.