Quantum Thermodynamics of an $\alpha^{\prime}$-Corrected Reissner-Nordstr\"om Black Hole

TL;DR

This paper investigates how $4$ corrections influence the thermodynamics, stability, and quantum properties of Reissner-Nordstrf6m black holes, introducing a corrected first law and analyzing non-equilibrium quantum effects.

Contribution

It introduces a novel $4$-corrected first law and analyzes quantum thermodynamics and stability of black holes with quantum gravitational corrections.

Findings

$4$ corrections modify black hole thermodynamics and stability.

Quantum work distribution is calculated using Ramsey scheme.

Corrected free energies relate to quantum work via Jarzynski equality.

Abstract

In this paper, we will analyze the effects of $\alpha^{\prime} $ corrections on the behavior of a Reissner-Nordstr\"{o}m black hole. We will calculate the effects of such corrections on the thermodynamics and thermodynamic stability of such a black hole. We will also derived a novel $\alpha^{\prime}$-corrected first law. We will investigate the effect of such corrections on the Parikh-Wilczek formalism. This will be done using cross entropy and Kullback-Leibler divergence between the original probability distribution and the $\alpha^{\prime}$-corrected probability distribution. We will then analyze the non-equilibrium quantum thermodynamics of this black hole. It will be observed that its quantum thermodynamics is corrected due to quantum gravitational corrections. We will use Ramsey scheme for emitted particles to calculate the quantum work distribution for this system. The average quantum work will be related to the difference of $\alpha^{\prime}$-corrected free energies using the Jarzynski equality.