Quantum coarse-grained entropy and thermodynamics

TL;DR

This paper introduces a quantum version of coarse-grained entropy that aligns with thermodynamic entropy in equilibrium and long-time limits, resolving a key conceptual issue in quantum thermodynamics.

Contribution

It develops two quantum coarse-grainings based on local measurements, extending classical entropy concepts to the quantum domain and addressing the second law in isolated systems.

Findings

Entropy reaches thermodynamic values in long-time limits

Entropy is consistent with thermodynamics outside equilibrium

Potential for experimental measurement of the quantum entropy

Abstract

We extend classical coarse-grained entropy, commonly used in many branches of physics, to the quantum realm. We find two coarse-grainings, one using measurements of local particle numbers and then total energy, and the second using local energy measurements, which lead to an entropy that is defined outside of equilibrium, is in accord with the thermodynamic entropy for equilibrium systems, and reaches the thermodynamic entropy in the long-time limit, even in genuinely isolated quantum systems. This answers the long-standing conceptual problem, as to which entropy is relevant for the formulation of the second thermodynamic law in closed quantum systems. This entropy could be in principle measured, especially now that experiments on such systems are becoming feasible.