Increase of quantum volume entropy in presence of degenerate eigenenergies

TL;DR

This paper extends the concept of volume entropy in quantum systems to include cases with degenerate eigenenergies, demonstrating that the entropy does not decrease on average even with degeneracies present.

Contribution

It introduces a quantum volume entropy framework that accounts for degeneracies in eigenenergies, broadening previous non-degenerate spectrum results.

Findings

Quantum volume entropy does not decrease on average with degeneracies.

Extension of classical and quantum entropy results to degenerate spectra.

Provides a more general understanding of entropy behavior in quantum systems.

Abstract

The entropy of a classical thermally isolated Hamiltonian system is given by the logarithm of the measure of phase space enclosed by the constant energy hyper-surface, also known as volume entropy. It has been shown that on average the latter cannot decrease if the initial state is sampled from a classical passive distribution. Quantum extension of this result has been shown, but only for systems with a non-degenerate energy spectrum. Here we further extend to the case of possible degeneracies.