Improved upper bound to the entropy of a charged system

Recently, we derived an improved universal upper bound to the entropy of a charged system $S<~\pi \left(2\mathrm{Eb}-q^2\right)/ħ.$ 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.