Black hole thermodynamics in finite time

TL;DR

This paper applies finite-time thermodynamics and geometric methods to analyze the energy dissipation in realistic, non-reversible processes involving black holes, specifically focusing on Kerr black holes losing mass and angular momentum.

Contribution

It introduces a geometric thermodynamics framework to quantify energy dissipation in finite-time black hole processes, extending finite-time thermodynamics to black hole physics.

Findings

Derived a lower bound on energy dissipation during black hole processes.

Applied thermodynamic length to black hole scenarios inspired by the Penrose process.

Quantified finite-time effects on black hole energy extraction efficiency.

Abstract

Finite-time thermodynamics provides the means to revisit ideal thermodynamic equilibrium processes in the light of reality and investigate the energetic "price of haste", i.e. the consequences of carrying out a process in finite time, when perfect equilibrium cannot be awaited due to economic reasons or the nature of the process. Employing the formalism of geometric thermodynamics, a lower bound on the energy dissipated during a process is derived from the thermodynamic length of that process. The notion of length is hereby defined via a metric structure on the space of equilibrium thermodynamics, spanned by a set of thermodynamic variables describing the system. Since the aim of finite-time thermodynamics is to obtain realistic limitations on idealized scenarios, it is a useful tool to reassess the efficiency of thermodynamic processes. We examine its implications for black hole thermodynamics, in particular scenarios inspired by the Penrose process, a thought experiment by which work can be extracted from a rotating black hole. We consider a Kerr black hole which, by some mechanism, is losing mass and angular momentum. Thermodynamically speaking, such a process is described in the equilibrium phase space of the black hole, but in reality, it is neither reversible nor infinitely slow. We thus calculate the dissipated energy due to non-ideal finite-time effects.