Improved Upper Bound to the Entropy of a Charged System

TL;DR

This paper refines the upper bound on the entropy of a charged system by precisely deriving the numerical factor through a thermodynamic gedanken experiment, considering spacetime curvature effects.

Contribution

It provides a more accurate upper bound on charged system entropy by removing previous uncertainties and incorporating spacetime curvature effects in the derivation.

Findings

Refined the entropy upper bound with a precise numerical factor.

Included spacetime curvature effects in electrostatic self-interaction analysis.

Confirmed the bound's consistency with the generalized second law.

Abstract

Recently, we derived an improved universal upper bound to the entropy of a charged system $S \leq \pi (2E b-q^2)/ \hbar$. There was, however, some uncertainty in the value of the numerical factor which multiplies the $q^2$ term. In this paper we remove this uncertainty; we rederive this upper bound from an application of the generalized second law of thermodynamics to a gedanken experiment in which an entropy-bearing charged system falls into a Schwarzschild black hole. A crucial step in the analysis is the inclusion of the effect of the spacetime curvature on the electrostatic self-interaction of the charged system.