Revising the quantum work fluctuation framework to encompass energy conservation

TL;DR

This paper revises the quantum work fluctuation framework to incorporate energy conservation, introducing a quantum correction to the Jarzynski equality and developing measurement schemes that ensure energy conservation in quantum systems.

Contribution

It introduces a quantum correction to the Jarzynski equality that accounts for energy conservation, addressing limitations in previous definitions of quantum work.

Findings

Quantum correction modifies the Jarzynski equality.

Measurement schemes certify energy conservation.

Quantum work can violate the second law more often.

Abstract

Work is a process-based quantity, and its measurement typically requires interaction with a measuring device multiple times. While classical systems allow for non-invasive and accurate measurements, quantum systems present unique challenges due to the influence of the measuring device on the final value of work. As recent studies have shown, among these challenges is the impossibility of formulating a universal definition of work that respects energy conservation for coherent quantum systems and is compatible with the Jarzynski equality - a fluctuation relation linking the equilibrium free energy difference to the non-equilibrium work. Here we overcome this challenge by introducing a genuinely quantum, positive correction to the Jarzynski equality stemming from imposing energy conservation. When sufficiently large, this correction forces quantum work to violate the second law more often. Moreover, we construct modified two-point measurement (TPM) schemes for work along with circuit implementations for them. These measurement schemes correctly certify energy conservation and remain consistent with our quantum-corrected fluctuation relation.