Does the generalized second law require entropy bounds for a charged system?

TL;DR

This paper extends the analysis of the generalized second law to charged systems, showing that equilibrium conditions of the thermal atmosphere and matter properties suffice to prevent violations, without needing entropy bounds.

Contribution

It demonstrates that entropy bounds are unnecessary for charged systems in gedanken experiments, relying instead on thermal atmosphere properties and matter equilibrium conditions.

Findings

Thermal atmosphere properties are crucial when charge is present.

Equilibrium conditions suffice to uphold the generalized second law.

No additional entropy bounds are required for charged systems.

Abstract

We calculate the net change in generalized entropy occurring when one carries out the gedanken experiment in which a box initially containing energy $E$, entropy $S$ and charge $Q$ is lowered adiabatically toward a Reissner-Nordstr\"{o}m black hole and then dropped in. This is an extension of the work of Unruh-Wald to a charged system (the contents of the box possesses a charge $Q$). Their previous analysis showed that the effects of acceleration radiation prevent violation of the generalized second law of thermodynamics. In our more generic case, we show that the properties of the thermal atmosphere are equally important when charge is present. Indeed, we prove here that an equilibrium condition for the the thermal atmosphere and the physical properties of ordinary matter are sufficient to enforce the generalized second law. Thus, no additional assumptions concerning entropy bounds on the contents of the box need to be made in this process. The relation between our work and the recent works of Bekenstein and Mayo, and Hod (entropy bound for a charged system) are also discussed.