Quantum thermodynamics of an Reissner-Nordström black hole

¹ School of Physics, Damghan University - Damghan, 3671641167, Iran
² Physics Department, Istanbul Technical University - Istanbul, 34469, Turkey
³ Physics Department, Eastern Mediterranean University - Famagusta 99628, North Cyprus, via Mersin 10, Turkey
⁴ Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan Kelowna, BC V1V 1V7, Canada
⁵ Canadian Quantum Research Center - 204-3002 32 Ave, Vernon, BC V1T 2L7, Canada
⁶ Department of Physics Engineering, Istanbul Technical University - Istanbul, 34469, Turkey

^(a) E-mail: b.pourhassan@du.ac.ir
^(b) E-mail: izzet.sakalli@emu.edu.tr
^(c) E-mail: xiaoping.shi@ubc.ca
^(d) E-mail: mirfaizalmir@gmail.com (corresponding author)
^(e) E-mail: salmansajadwani@gmail.com

Received: 19 July 2023
Accepted: 4 October 2023

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.