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Black hole thermodynamics at null infinity. II. Open systems, Markovian dynamics, and work extraction from nonrotating black holes

Antoine Rignon-Bret1,* and Matthieu Vilatte2,†

  • *Contact author: arignonbret@gmail.com
  • †Contact author: matthieu.vilatte@umons.ac.be
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Phys. Rev. D 114, 065011 – Published 10 September, 2026

DOI: https://doi.org/10.1103/py7c-gxvw

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 nonexpanding 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 [A. Rignon-Bret and M. Vilatte, companion paper, Phys. Rev. D 114, 065012 (2026)], we show that additional terms appearing in the associated thermodynamic potentials admit a natural interpretation as work contributions. We demonstrate that certain nonthermal 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 graybody 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.

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Black hole thermodynamics at null infinity. I. Dual generalized second law

Antoine Rignon-Bret and Matthieu Vilatte
Phys. Rev. D 114, 065012 (2026)

Article Text

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Phys. Rev. D 114, 065011– Published 10 September, 2026
  • Received 9 March 2026
  • Accepted 3 August 2026
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