Holographic second laws of black hole thermodynamics

TL;DR

This paper explores new quantum thermodynamic constraints, called holographic second laws, in black hole physics using the AdS/CFT correspondence, revealing restrictions on black hole dynamics beyond the traditional area increase law.

Contribution

It introduces a holographic approach to quantum second laws of thermodynamics in black holes, linking Renyi divergences to gravitational dynamics via Euclidean path integrals.

Findings

Renyi divergence computed through Euclidean path integrals.

Additional thermodynamic constraints restrict black hole transitions.

Certain transitions allowed by the second law are forbidden by the new constraints.

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 R\'enyi 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 R\'enyi 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 R\'enyi 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.