Holographic Second Laws of Black Hole Thermodynamics

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General Non-equilibrium Statistical Physics

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authors

Alice Bernamonti

Federico Galli

Robert C. Myers

Jonathan Oppenheim

title

Holographic Second Laws of Black Hole Thermodynamics

type

journal

year

2018

pages

70

volume

2018

issue

6

publisher

Springer Nature

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.

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Identifiers

• doi: https://doi.org/10.1007/JHEP07(2018)111 (Google search)
• issn: 1029-8479
• arxiv: https://arxiv.org/abs/1803.03633
• websites: https://link.springer.com/article/10.1007/JHEP07(2018)111