Black hole thermodynamics at null infinity. Part 2: Open systems, Markovian dynamics and work extraction from non-rotating black holes

TL;DR

This paper explores the thermodynamics of quantum fields near black hole horizons, establishing a framework that links black hole physics with open quantum system dynamics and demonstrating the possibility of work extraction from black hole radiation.

Contribution

It introduces a novel dictionary connecting black hole boundary conditions with open quantum system concepts and extends thermodynamic laws to include work extraction and grey body effects.

Findings

Work can be extracted from non-thermal vacuum states at null infinity.

Generalized grand potential laws incorporate grey body effects and angular momentum fluxes.

Black hole thermodynamics can be understood within the framework of open quantum thermodynamics.

Abstract

Black hole thermodynamics provides a unique setting in which general relativity, quantum field theory, and statistical mechanics converge. In semiclassical gravity, this interplay culminates in the generalized second law (GSL), whose modern proofs rely on information theoretic techniques applied to algebras of observables defined on null hypersurfaces. These proofs exhibit close structural parallels with the thermodynamics of open quantum systems governed by Markovian dynamics. In this work, we draw parallels between the dynamics of quantum fields in regions bounded by non expanding causal horizons and the thermodynamics of quantum systems weakly coupled to equilibrium reservoirs. We introduce a dictionary relating late time boundary conditions to the choice of reservoir, vacuum states to fixed points of the dynamics, and modular Hamiltonians to thermodynamic potentials. Building on results from a companion paper on dual generalized second laws at future null infinity, we show that additional terms appearing in the associated thermodynamic potentials admit a natural interpretation as work contributions. We demonstrate that certain non thermal vacuum states at null infinity allow for the operation of autonomous thermal engines and enable work extraction from the radiation. Extending the analysis to the Unruh vacuum in Schwarzschild and Kerr backgrounds, we obtain generalized grand potential type laws incorporating grey body effects and angular momentum fluxes. Altogether, our results clarify the thermodynamic description of black hole dynamics and place it within the broader framework of open quantum thermodynamics.