A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
By Aron C. Wall. 2011
260 citations recorded by the source corpus.
The generalized second law is proven for semiclassical quantum fields falling across a causal horizon, minimally coupled to general relativity. The proof is much more general than previous proofs in that it permits the quantum fields to be rapidly changing with time, and shows that entropy increases when comparing any slice of the horizon to any earlier slice. The proof requires the existence of an algebra of observables restricted to the horizon, satisfying certain axioms (Determinism, Ultralocality, Local Lorentz Invariance, and Stability). These axioms are explicitly verified in the case of free fields of various spins, as well as 1+1 conformal field theories. The validity of the axioms for other interacting theories is discussed.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/23def4a6b3ae45a4be13552d2f14f199df593a07
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Citations in the corpus
- An algebra of observables for de Sitter space (2022, methodology): “We also make use of a formula of Wall expressing the generalized entropy in terms of relative entropy on the horizon [33].”
- Relative entropy equals bulk relative entropy (2015, background): “It has also played an important role in formulating a precise version of the Bekenstein bound [3] and arguments for the second law of black hole thermodynamics [4, 5].”
- APS Medal for Exceptional Achievement in Research: Invited article on entanglement properties of quantum field theory (2018, background): “The more subtle property of monotonicity of relative entropy, to which we come next, also has various applications, for instance in the proof of a semiclassical generalized second law of thermodynamics that includes black hole entropy (Wall, 2012).”
- Quantum extremal islands made easy. Part I. Entanglement on the brane (2020, background): “As emphasized with the generalized second law [15] (see also [16, 17]), the geometric BH entropy is naturally combined with the entanglement entropy of quantum fields outside the event horizon to produce a finite quantity known as the generalized entropy.”
- Jerusalem Lectures on Black Holes and Quantum Information (2014, background): “3) as stated has several problems [73], but a more general covariant version of it [79, 80] has survived many quantitative tests and been proven to hold in a wide variety of classical and semiclassical situations [81–84].”
- Modular Hamiltonians for deformed half-spaces and the averaged null energy condition (2016, methodology): “Wall has also argued that the ANEC holds true for free or superrenormalizable field theories in general dimension [16].”
- Notes on Some Entanglement Properties of Quantum Field Theory (2018, background): “The more subtle property of monotonicity of relative entropy, to which we come next, also has various applications, for instance in the proof of a semiclassical generalized second law of thermodynamics that includes black hole entropy [52].”
- A general proof of the quantum null energy condition (2017, background): “Wall [13] based on light front quantization.”
- Traversable wormholes via a double trace deformation (2016, methodology): “For since the GSL is true in every state [54], and saturated for the Hartle-Hawking state, it must also be saturated for any first order perturbation to the Hartle-Hawking state [52].”
- Analyticity and the Unruh effect: a study of local modular flow (2024, background): “The reason this can be done to move from the domain in figure 6 to the domain in figure 7 is a consequence of a general theorem due to Vladimirov called the C-convex hull theorem [41, section 28].”
- Modular Hamiltonians on the null plane and the Markov property of the vacuum state (2017, background): “A central charge term is in principle also possible, however, the central charge is UV divergent on dimensional grounds [22]8.”
- Recovering the QNEC from the ANEC (2018, background): “For other null cuts the vacuum modular Hamiltonian’s have been the subject of recent investigation [5, 20, 36, 37].”
- Symmetries and charges of general relativity at null boundaries (2018, background): “17 We will call (17)This supertranslation subgroup of symmetries played an important role in Wall’s proof of the generalized second law [27].”