Thermodynamics at Null Infinity Enables Work Extraction from Non-Rotating Black Holes

Black holes present a fascinating intersection of general relativity, field theory and statistical mechanics, and recent research continues to refine our understanding of their thermodynamic properties. Antoine Rignon-Bret of the Université de Lorraine and Matthieu Vilatte of UMONS, along with their colleagues, have explored the connection between black hole dynamics and the thermodynamics of open systems. Their work draws parallels between fields near causal horizons and systems interacting with equilibrium reservoirs, establishing a clear relationship between boundary conditions, vacuum states and thermodynamic potentials. This research is significant because it not only clarifies the thermodynamic description of black holes, but also demonstrates the possibility of extracting work from their radiation using specific non-thermal vacuum states. By extending analysis to Schwarzschild and Kerr backgrounds, the team provides a more complete framework for understanding black hole thermodynamics within the broader context of open thermodynamic systems.

Quantum field theory, statistical mechanics and semiclassical gravity converge in explorations of fundamental physics. Modern proofs of the generalized second law (GSL) rely on information-theoretic techniques applied to algebras of observables defined on null hypersurfaces, revealing structural parallels with the thermodynamics of open quantum systems governed by Markovian dynamics. This work draws explicit 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, introducing a dictionary relating late-time boundary conditions to the choice of reservoir.

Black Hole Entropy via Open Quantum System Mapping

The study establishes a connection between black hole thermodynamics and the thermodynamics of open quantum systems, pioneering a novel approach to understanding gravitational entropy. Researchers drew parallels between the dynamics of fields near non-expanding causal horizons and systems weakly coupled to equilibrium reservoirs, introducing a precise ‘dictionary’ to relate concepts between these seemingly disparate fields. Specifically, late-time boundary conditions were mapped onto reservoir choices, vacuum states corresponded to fixed points of the dynamics, and modular Hamiltonians were equated with thermodynamic potentials, enabling a consistent thermodynamic description of black hole behaviour. To rigorously examine these connections, the team built upon prior work concerning dual generalized second laws at future null infinity, demonstrating that additional terms appearing in thermodynamic potentials can be naturally interpreted as contributions from work.

Experiments employed massless scalar fields on maximally extended null infinity, alongside the Hartle-Hawking state and its regularizations, to investigate the dual generalized second law using quantum relative entropy, achieving a precise formulation and derivation of the generalized second law mirroring techniques used in open quantum systems. Further innovation came with the analysis of work extraction from a non-rotating black hole, revealing that certain non-thermal vacuum states at null infinity permit the operation of autonomous thermal engines. Scientists constructed the Unruh vacuum in both Schwarzschild and Kerr backgrounds, obtaining generalized grand potential laws that incorporate grey body effects and angular momentum fluxes, allowing exploration of the second law within this specific vacuum state. Extending this analysis to the Kerr black hole, the study developed a vacuum state tailored to the rotating spacetime and subsequently examined the validity of the second law in this complex background.

Black Holes, Quantum Systems and Thermal Engines

Scientists have established a compelling connection between black hole thermodynamics and the principles governing open quantum systems, revealing a shared mathematical structure. The research demonstrates parallels between the dynamics of quantum fields near non-expanding causal horizons and the thermodynamics of systems weakly coupled to equilibrium reservoirs. A key achievement of this work is the development of a ‘dictionary’ linking late-time boundary conditions to reservoir choices, vacuum states to fixed points in the dynamics, and modular Hamiltonians to thermodynamic potentials. Experiments revealed that specific non-thermal vacuum states at null infinity permit the operation of autonomous thermal engines, successfully extracting work from the surrounding radiation.

The team measured work contributions arising from additional terms in the associated thermodynamic potentials, clarifying their interpretation within the framework of open thermodynamics. Extending this analysis to the Unruh vacuum in both Schwarzschild and Kerr backgrounds, researchers obtained generalized grand potential-type laws that incorporate grey body effects and angular momentum fluxes, providing a more complete thermodynamic description. Further investigation into the Unruh vacuum allowed scientists to construct a vacuum state for Kerr black holes and subsequently examine the second law of thermodynamics in this complex background. The study details how the generalized second law, expressed as ΔSgen = ΔA/4G + Sout ≥0, is maintained, where ΔA represents the change in the area of the event horizon and Sout denotes the entropy of matter fields outside the black hole.

This work clarifies the thermodynamic description of black hole dynamics, placing it firmly within the broader context of open quantum thermodynamics and offering new insights into gravitational entropy. The research builds upon previous findings concerning dual generalized second laws at future null infinity, solidifying the link between quantum information theory and black hole physics. By applying techniques from quantum information theory to quantum fields, the team rigorously formulated and derived the generalized second law, demonstrating its connection to the monotonicity of quantum relative entropy, and highlighting the importance of identifying appropriate stationary reference states.

Black Holes, Open Quantum Systems and Work Extraction

This work establishes a compelling connection between black hole dynamics and the thermodynamics of open quantum systems. By drawing parallels between fields evolving in regions bounded by causal horizons and systems weakly coupled to reservoirs, the researchers have constructed a dictionary linking late-time boundary conditions to reservoir choices, vacuum states to fixed points, and modular Hamiltonians to thermodynamic potentials. This framework successfully interprets additional terms arising in thermodynamic potentials as contributions from work, demonstrating the possibility of extracting work from radiation using specific non-thermal vacuum states at null infinity. Further extending their analysis to Schwarzschild and Kerr backgrounds, the team derived generalized grand potential laws that incorporate effects like grey body radiation and angular momentum fluxes. These results clarify the thermodynamic description of black holes, positioning their dynamics firmly within the broader context of open thermodynamics. The authors acknowledge limitations stemming from the approximations inherent in treating the black hole environment as a weakly coupled reservoir, and note that the analysis focuses on specific vacuum states, suggesting future research could explore the implications for a deeper understanding of gravitational entropy and the information loss paradox.