Non-Equilibrium Physics of Thermodynamicized Black Holes

TL;DR

This paper develops a non-equilibrium thermodynamic framework for black holes, incorporating entropy functionals, topological classifications, and flux effects, extending standard equilibrium relations to dynamic black hole systems.

Contribution

It introduces a novel non-equilibrium formalism for black hole thermodynamics, unifying entropy functionals, topological residue classification, and flux-driven corrections in a consistent framework.

Findings

Reproduces equilibrium relations in the adiabatic limit.

Extends thermodynamics to dynamical black holes with matter, charge, and rotation.

Shows topological differences between inner and outer horizons in Kerr-Newman black holes.

Abstract

This work presents a non-equilibrium framework for thermodynamicized black holes, inspired by the entropy-functional interpretation of emergent gravity and by residue-based methods in black hole thermodynamics. The main idea is to unify three components: an entropy functional principle for selecting physical on-shell backgrounds, a Euclidean and contour-based description of the horizon temperature through simple pole singularities, and a topological residue classification of multi-horizon black hole configurations. On this basis, the paper introduces a quasi-stationary non-equilibrium partition functional in which irreversible entropy production appears as an additional contribution to the singular action. The formalism reproduces the standard equilibrium relations in the adiabatic limit, while also extending them to dynamically driven black-hole systems with matter, charge, and rotational fluxes. The framework is then applied to Kerr Newman type black holes in constant curvature f(R) gravity, where the equilibrium entropy remains weighted by the derivative of f at the background curvature, while non-equilibrium corrections arise from flux-induced deformations of the effective thermodynamic action. The analysis further shows that the outer and inner horizons carry opposite topological orientations, so the non-extremal Kerr Newman family stays in the topological class W = 0 unless a horizon bifurcation or merger changes the singularity structure. Finally, several function plots are provided to illustrate the behavior of equilibrium and non-equilibrium free energy, the Kerr Newman temperature curve, and the entropy production law.