Entropy functionals and c-theorems from the second law

TL;DR

This paper demonstrates that holographic entanglement entropy functionals uniquely obey the second law at linear order in four-derivative gravity theories and derives bounds on higher curvature couplings from second law validity, linking to stability and causality constraints.

Contribution

It establishes the special role of holographic entanglement entropy functionals in obeying the second law and derives bounds on higher curvature couplings from second law considerations, connecting to stability and causality.

Findings

Holographic entanglement entropy functionals obey the second law at linear order.

Bounds on higher curvature couplings are derived from second law validity.

Connections between second law, stability, and causality constraints are established.

Abstract

We show that for a general four derivative theory of gravity, only the holographic entanglement entropy functionals obey the second law at linearized order in perturbations. We also derive bounds on the higher curvature couplings in several examples, demanding the validity of the second law for higher order perturbations. For the five dimensional Gauss-Bonnet theory in the context of AdS/CFT, the bound arising from black branes coincides with there being no sound channel instability close to the horizon. Repeating the analysis for topological black holes, the bound coincides with the tensor channel causality constraint (which is responsible for the viscosity bound). Furthermore, we show how to recover the holographic c-theorems in higher curvature theories from similar considerations based on the Raychaudhuri equation.