Validity of the second law in nonextensive quantum thermodynamics

TL;DR

This paper investigates the validity of the second law of thermodynamics within nonextensive quantum thermodynamics, demonstrating that Clausius' inequality holds for a specific range of the entropic index q, highlighting quantum-specific constraints.

Contribution

It establishes the conditions under which the second law remains valid in nonextensive quantum systems, emphasizing the role of the entropic index q and its quantum limitations.

Findings

Clausius' inequality holds for 0 < q < 2 in quantum systems.

No upper bound of q for the second law's validity in classical thermodynamics.

Quantum convexity properties are key to these results.

Abstract

The second law of thermodynamics in nonextensive statistical mechanics is discussed in the quantum regime. Making use of the convexity property of the generalized relative entropy associated with the Tsallis entropy indexed by q, Clausius' inequality is shown to hold in the range of q between zero and two. This restriction on the range of the entropic index, q, is purely quantum mechanical and there exists no upper bound of q for validity of the second law in classical theory.