Leggett-Garg inequalities for quantum fluctuating work

TL;DR

This paper derives Leggett-Garg inequalities for quantum work fluctuations and demonstrates their violation in a two-level system, revealing fundamental differences between quantum and classical thermodynamics.

Contribution

It introduces Leggett-Garg inequalities for quantum work statistics and shows their violation, challenging macrorealistic explanations of quantum thermodynamics.

Findings

Violations occur in driven two-level systems.

Violations are present under both projective and weak measurements.

Highlights fundamental quantum-classical differences in thermodynamics.

Abstract

The Leggett-Garg inequalities serve to test whether or not quantum correlations in time can be explained within a classical macrorealistic framework. We apply this test to thermodynamics and derive a set of Leggett- Garg inequalities for the statistics of fluctuating work done on a quantum system unitarily driven in time. It is shown that these inequalities can be violated in a driven two-level system, thereby demonstrating that there exists no general macrorealistic description of quantum work. These violations are shown to emerge within the standard Two-Projective-Measurement scheme as well as for alternative definitions of fluctuating work that are based on weak measurement. Our results elucidate the influences of temporal correlations on work extraction in the quantum regime and highlight a key difference between quantum and classical thermodynamics.