A note on the connection between the universal relaxation bound and the covariant entropy bound

TL;DR

This paper explores the relationship between the universal relaxation bound and the covariant entropy bound, revealing a statistical-mechanical property that explains the bound's universality across different systems, including black holes and non-black hole systems.

Contribution

It identifies a lower-limiting size for thermodynamic systems that underpins the universal relaxation bound, linking quantum information theory, thermodynamics, and gravity.

Findings

Lower size limit l* explains relaxation bound

Black holes saturate the relaxation bound

Non-black hole systems can also saturate the bound

Abstract

A recently proposed universal lower-bound to the characteristic relaxation times of perturbed thermodynamic systems, derived from quantum information theory and (classical) thermodynamics and known to be saturated for (certain) black holes, is investigated in the light of the gravity/thermodynamics connection. A statistical-mechanical property, unrelated to gravity, essential for the validity of the generalized covariant entropy bound, namely the existence of a lower-limiting value l* for the size of thermodynamic systems, is found to provide a way to understand the universal relaxation bound, thus regardless of the kind of foundations (i.e. whether conventional or information-based) of the statistical-mechanical description. As a by-product an example of a conventional system (i.e. not a black hole) seemingly saturating the universal relaxation bound is provided.