Holographic second laws of black hole thermodynamics

Abstract

Recently, it has been shown that for out-of-equilibrium systems, there are additional constraints on thermodynamical evolution besides the ordinary second law. These form a new family of second laws of thermodynamics, which are equivalent to the monotonicity of quantum Rényi divergences. In black hole thermodynamics, the usual second law is manifest as the area increase theorem. Hence one may ask if these additional laws imply new restrictions for gravitational dynamics, such as for out-of-equilibrium black holes? Inspired by this question, we study these constraints within the AdS/CFT correspondence. First, we show that the Rényi divergence can be computed via a Euclidean path integral for a certain class of excited CFT states. Applying this construction to the boundary CFT, the Rényi divergence is evaluated as the renormalized action for a particular bulk solution of a minimally coupled gravity-scalar system. Further, within this framework, we show that there exist transitions which are allowed by the traditional second law, but forbidden by the additional thermodynamical constraints. We speculate on the implications of our findings.

81 pages, 19 figures; v2: clarifications and reference added, minor typos corrected, published version

References in corpus (20)

• Description of quantum coherence in thermodynamic processes requires constraints beyond free energy
• Quantum coherence, time-translation symmetry and thermodynamics
• The thermodynamic meaning of negative entropy
• Horizon formation and far-from-equilibrium isotropization in supersymmetric Yang-Mills plasma
• Thermalization of Strongly Coupled Field Theories
• Setting the boundary free in AdS/CFT
• Holographic Evolution of Entanglement Entropy
• Deriving covariant holographic entanglement
• Holographic Entanglement Entropy from 2d CFT: Heavy States and Local Quenches
• Evolution of Holographic Entanglement Entropy after Thermal and Electromagnetic Quenches
• Quantum Entanglement of Localized Excited States at Finite Temperature
• Relative Entropies in Conformal Field Theory
• From Euclidean Sources to Lorentzian Spacetimes in Holographic Conformal Field Theories
• A proof of the generalized second law for rapidly-evolving Rindler horizons
• Ten Proofs of the Generalized Second Law
• On holographic thermalization and gravitational collapse of massless scalar fields
• Relative Entanglement Entropies in 1+1-dimensional conformal field theories
• Thermalization after holographic bilocal quench
• Holographic Quenches in a Confined Phase
• Holographic Quenches and Fermionic Spectral Functions

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