Quantum work fluctuations versus macrorealism in terms of non-extensive entropies

TL;DR

This paper explores how non-extensive Tsallis entropies can be used to distinguish quantum from classical work fluctuations and detect violations of macrorealism, accounting for measurement inefficiencies.

Contribution

It introduces a novel entropic approach using Tsallis entropies to analyze quantum work fluctuations and macrorealism violations, enhancing robustness and incorporating measurement losses.

Findings

Tsallis entropies improve detection of macrorealism violations.

The approach accounts for measurement inefficiencies.

Generalized entropies offer advantages in quantum fluctuation analysis.

Abstract

Fluctuations of the work performed on a driven quantum system can be characterized by the so-called fluctuation theorems. The Jarzynski relation and the Crooks theorem are famous examples of exact equalities characterizing non-equilibrium dynamics. Such statistical theorems are typically formulated in a similar manner in both classical and quantum physics. Leggett-Garg inequalities are inspired by the two assumptions referred to as the macroscopic realism and the non-invasive measurability. Together, these assumptions are known as the macrorealism in the broad sense. Quantum mechanics is provably incompatible with restrictions of the Leggett-Garg type. It turned out that Leggett-Garg inequalities can be used to distinguish quantum and classical work fluctuations. We develop this issue with the use of entropic functions of the Tsallis type. Varying the entropic parameter, we are often able to reach more robust detection of violations of the corresponding Leggett-Garg inequalities. In reality, all measurement devices suffer from losses. Within the entropic formulation, detection inefficiencies can naturally be incorporated into the consideration. This question also shows advantages that are provided due to the use of generalized entropies.