Quantum mechanical work

TL;DR

This paper develops a quantum mechanical framework for defining work as an observable, demonstrating its consistency with classical limits and exploring implications for quantum thermodynamics and measurement protocols.

Contribution

It introduces a well-defined quantum work operator with eigensystems, enabling new perspectives on quantum superposition and nonlocal effects in work measurement.

Findings

Work can be represented as a quantum observable with a clear classical limit.

Two-point measurement protocols may be inadequate in the semiclassical regime.

A work-energy uncertainty relation is derived, linking quantum work and energy conservation.

Abstract

Regarded as one of the most fundamental concepts of classical mechanics and thermodynamics, work has received well-grounded definitions within the quantum framework since the 1970s, having being successfully applied to many contexts. Recent developments on the concept have taken place in the emergent field of quantum thermodynamics, where work is frequently characterized as a stochastic variable. Notwithstanding this remarkable progress, it is still debatable whether some sensible notion of work can be posed for a strictly quantum instance involving a few-particle system prepared in a pure state and abandoned to its closed autonomous dynamics. By treating work as a quantum mechanical observable with a well defined classical limit, here we show that this scenario can be satisfactorily materialized. We prove, by explicit examples, that one can indeed assign eigensystems to work operators. This paves the way for frameworks involving quantum superposition and nonlocal steering of work. We also show that two-point measurement protocols can be inappropriate to describe work (and other two-time physical quantities), especially in the semiclassical regime. However subtle it may be, our quantum mechanical notion of work is experimentally testable and requires an updating of our intuition regarding the concept of two-time elements of reality. In this context, we derive a work-energy uncertainty relation, and we illustrate how energy conservation emerges as an element of physical reality.