Ten Proofs of the Generalized Second Law

Abstract

Ten attempts to prove the Generalized Second Law of Thermodyanmics (GSL) are described and critiqued. Each proof provides valuable insights which should be useful for constructing future, more complete proofs. Rather than merely summarizing previous research, this review offers new perspectives, and strategies for overcoming limitations of the existing proofs. A long introductory section addresses some choices that must be made in any formulation the GSL: Should one use the Gibbs or the Boltzmann entropy? Should one use the global or the apparent horizon? Is it necessary to assume any entropy bounds? If the area has quantum fluctuations, should the GSL apply to the average area? The definition and implications of the classical, hydrodynamic, semiclassical and full quantum gravity regimes are also discussed. A lack of agreement regarding how to define the "quasi-stationary" regime is addressed by distinguishing it from the "quasi-steady" regime.

60 pages, 2 figures, 1 table. v2: corrected typos and added a footnote to match the published version

References in corpus (55)

• Black Hole Entropy is Noether Charge
• Entropy and Area
• The holographic principle
• Evanescent Black Holes
• A Covariant Entropy Conjecture
• The Thermodynamics of Black Holes
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Hawking Radiation and Black Hole Thermodynamics
• A finite entanglement entropy and the c-theorem
• The Endpoint of Hawking Evaporation
• Black Hole Entropy and Entropy of Entanglement
• Averaged Energy Conditions and Quantum Inequalities
• Entropy Bounds and Black Hole Remnants
• Dynamical Origin of the Entropy of a Black Hole
• Forks in the Road, on the Way to Quantum Gravity
• Black hole thermodynamics and information loss in two dimensions
• Proof of Classical Versions of the Bousso Entropy Bound and of the Generalized Second Law
• Renormalization of Black Hole Entropy and of the Gravitational Coupling Constant
• Increase of Black Hole Entropy in Higher Curvature Gravity
• Horizon Entropy
• Thermal Fields, Entropy, and Black Holes
• Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind
• Trans-Planckian redshifts and the substance of the space-time river
• On one-loop renormalization of black-hole entropy
• The "physical process" version of the first law and the generalized second law for charged and rotating black holes
• The generalized second law of thermodynamics in the accelerating universe
• Statistical Origin of Black Hole Entropy in Induced Gravity
• The Quantum Interest Conjecture
• One-loop Renormalization of Black Hole Entropy Due to Non-minimally Coupled Matter
• Proof of the Generalized Second Law for Quasistationary Semiclassical Black Holes
• Lorentz violation and perpetual motion
• Thermodynamics of Quantum Fields in Black Hole Backgrounds
• Wavefunction of a Black Hole and the Dynamical Origin of Entropy
• Notes on Spacetime Thermodynamics and the Observer-dependence of Entropy
• Simple sufficient conditions for the generalized covariant entropy bound
• Why is CPT fundamental?
• Black Hole Entropy in Two Dimensions
• Black Hole Entropy: Off-Shell vs On-Shell
• Light-sheets and Bekenstein's bound
• A Quantum Bousso Bound
• Renormalized black hole entropy in anti-de Sitter space via the "brick wall" method
• Classical Scalar Fields and the Generalized Second Law
• Large Fluctuations in the Horizon Area and what they can tell us about Entropy and Quantum Gravity
• On the Status of Highly Entropic Objects
• Renormalized Thermodynamic Entropy of Black Holes in Higher Dimensions
• From Unruh temperature to generalized Bousso bound
• The Renormalized Stress Tensor in Kerr Space-Time: Numerical Results for the Hartle-Hawking Vacuum
• Black hole entanglement entropy regularized in a freely falling frame
• Are there hyperentropic objects ?
• New Proof of the Generalized Second Law
• Black Hole Entropy: Thermodynamics, Statistical-Mechanics and Subtraction Procedure
• Comments on a Covariant Entropy Conjecture
• Renormalized Thermal Entropy in Field Theory
• A covariant entropy conjecture on cosmological dynamical horizon
• Note on Bound States and the Bekenstein Bound

Cited by in corpus (37)

• Thermodynamical Aspects of Gravity: New insights
• Quantum Extremal Surfaces: Holographic Entanglement Entropy beyond the Classical Regime
• Traversable Wormholes via a Double Trace Deformation
• A Quantum Focussing Conjecture
• Entanglement Equilibrium and the Einstein Equation
• A proof of the generalized second law for rapidly changing fields and arbitrary horizon slices
• Black Hole Thermodynamics
• The generalized second law of thermodynamics in Horava-Lifshitz cosmology
• The Many Definitions of a Black Hole
• Proving the Achronal Averaged Null Energy Condition from the Generalized Second Law
• Do gauge fields really contribute negatively to black hole entropy?
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Testing the Generalized Second Law in 1+1 dimensional Conformal Vacua: An Argument for the Causal Horizon
• Generalized second law at linear order for actions that are functions of Lovelock densities
• Generalized Second Law for Cosmology
• The holographic entropy increases in quadratic curvature gravity
• Semi-classical thermodynamics of quantum extremal surfaces in Jackiw-Teitelboim gravity
• Coarse-grained entropy and causal holographic information in AdS/CFT
• Solid/Liquid Phase Transition and Heat Engine in Asymptotically Flat Schwarzschild Black Hole via the Rényi Extended Phase Space Approach
• A Lower Bound on the Energy Density in Classical and Quantum Field Theories
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Renormalization group flow of entanglement entropy on spheres
• Holographic second laws of black hole thermodynamics
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• The Return of the Singularities: Applications of the Smeared Null Energy Condition
• Conformal Killing horizons and their thermodynamics
• Thermodynamics of Evolving Lorentzian Wormhole at Apparent and Event Horizons
• Gauge Invariant Derivation of Zeroth and First Laws of Black Hole Thermodynamics
• Generalised second law beyond the semiclassical regime
• On the Quantum Bousso Bound in JT gravity
• Horizon causality from holographic scattering in asymptotically dS${}_3$
• Island mirages
• Entropy increases at linear order in scalar-hairy Lovelock gravity
• Generalized Second Law for Non-minimally Coupled Matter Theories
• The generalized second law for fermionic and bosonic fields
• The generalized second law for Kerr-Taub-NUT black holes perturbed by test field
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group