ar X iv : g r - qc / 9 90 30 10 v 1 2 M ar 1 99 9 Universal Upper Bound to the Entropy of a Charged System

We derive a universal upper bound to the entropy of a charged system. The entropy bound follows from application of the generalized second law of thermodynamics to a gedanken experiment in which an entropy-bearing charged system falls into a charged black hole. This bound is stronger than the Bekenstein entropy bound for neutral systems. Black-hole physics mirrors thermodynamics in many respects [1–6]. According to the thermodynamical analogy in black-hole physics, the entropy of a black hole [7–9] is given by S bh = A/4¯ h, where A is the black-hole surface area. (We use gravitational units in which G = c = 1). Moreover, it is widely believed that a system consisting of ordinary matter interacting with a black hole will obey the generalized second law of thermodynamics (GSL): " The sum of the black-hole entropy and the common (ordinary) entropy in the black-hole exterior never decreases ". This assumption plays a fundamental role in black-hole physics. In a classical context, a basic physical mechanism is known by which a violation of the GSL can be achieved: Consider a box filled with matter of proper energy E and entropy S which is dropped into a black hole. The energy delivered to the black hole can be arbitrarily red-shifted by letting the assimilation point approach the black-hole horizon. As shown by Bekenstein [9,10], if the box is deposited with no radial momentum a proper distance R above the horizon, and then allowed to fall in such that 1