Quasi-local dynamical horizons admit a first law for finite, far-from-equilibrium processes and a quantitative second law tying area growth to energy fluxes, so black-hole entropy is the area of marginally trapped surfaces.
Rignon-Bret,Second law from the Noether current on null hypersurfaces,Phys
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Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.
In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; this lets the generalized second law be reinterpreted as matter entanglement across
The entropy of a dynamical black hole equals the area of its apparent horizon at second order in perturbations when the null energy condition holds.
citing papers explorer
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Thermodynamics of dynamical black holes beyond perturbation theory
Quasi-local dynamical horizons admit a first law for finite, far-from-equilibrium processes and a quantitative second law tying area growth to energy fluxes, so black-hole entropy is the area of marginally trapped surfaces.
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Holographic pressure and volume for black holes
Introduces a holographic pressure and volume for static spherically symmetric black holes via quasi-local thermodynamics, showing large black holes become extensive in the large-system limit while small ones do not.
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Entanglement Entropy and Thermodynamics of Dynamical Black Holes
In f(R) theories, the replica-method gravitational entropy computed on the apparent horizon matches the Hollands-Wald-Zhang dynamical black hole entropy and satisfies the first law, while the event horizon does not; this lets the generalized second law be reinterpreted as matter entanglement across
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The entropy of black hole under second-order deviation from equilibrium
The entropy of a dynamical black hole equals the area of its apparent horizon at second order in perturbations when the null energy condition holds.