Quantum thermodynamics of an Reissner-Nordström black hole

Abstract

In this paper, we will go beyond equilibrium description to properly investigate the evaporation of a Reissner-Nordström black hole. Thus, we will explicitly apply techniques of non-equilibrium quantum thermodynamics to this black hole. As the non-equilibrium effects would become important at the quantum scale, we will incorporate the quantum gravitational corrections by using an Reissner-Nordström black hole. We will start by developing a novel first law. Then we will investigate the quantum gravitational corrections to the Parikh-Wilczek formalism, and introduce Kullback-Leibler divergence to quantify the effects of corrections. Furthermore, we will demonstrate that the non-thermal nature of radiation in the Parikh-Wilczek formalism can be directly related to the average quantum work done on the emitted particles using non-equilibrium quantum thermodynamics. This is because the average quantum work done is a unitary process in non-equilibrium quantum thermodynamics. We will use the Ramsey scheme for emitted particles to calculate this quantum work distribution for the emitted particles.