Universal Bound on Dynamical Relaxation Times and Black-Hole Quasinormal Ringing

TL;DR

This paper establishes a universal lower bound on relaxation times based on thermodynamics and shows that black holes saturate this bound, making them the fastest relaxing objects in nature according to quantum limits.

Contribution

It proves that black holes exactly saturate the universal relaxation time bound derived from thermodynamic principles.

Findings

Black holes obey the relaxation time bound.

Black holes saturate the bound, indicating maximum relaxation rate.

Black holes are the most extreme relaxation objects in nature.

Abstract

From information theory and thermodynamic considerations a universal bound on the relaxation time $\tau$ of a perturbed system is inferred, $\tau \geq \hbar/\pi T$, where $T$ is the system's temperature. We prove that black holes comply with the bound; in fact they actually {\it saturate} it. Thus, when judged by their relaxation properties, black holes are the most extreme objects in nature, having the maximum relaxation rate which is allowed by quantum theory.