Quantum work and the thermodynamic cost of quantum measurements

TL;DR

This paper proposes a measurement-free definition of quantum work based on energy expectation changes, addressing the thermodynamic cost of measurements and deriving modified fluctuation relations.

Contribution

It introduces a new paradigm for quantum work that omits measurements, providing modified fluctuation relations and quantifying measurement costs.

Findings

Derived a modified quantum Jarzynski equality.

Formulated a sharpened maximum work theorem.

Quantified the informational cost of projective measurements.

Abstract

Quantum work is usually determined from two projective measurements of the energy at the beginning and at the end of a thermodynamic process. However, this paradigm cannot be considered thermodynamically consistent as it does not account for the thermodynamic cost of these measurements. To remedy this conceptual inconsistency we introduce a novel paradigm that relies only on the expected change of the average energy given the initial energy eigenbasis. In particular, we completely omit quantum measurements in the definition of quantum work, and hence quantum work is identified as a thermodynamic quantity of only the system. As main results we derive a modified quantum Jarzynski equality and a sharpened maximum work theorem in terms of the information free energy. Comparison of our results with the standard approach allows to quantify the informational cost of projective measurements.