From Thermodynamics to the Bound on Viscosity

Abstract

We show that the generalized second law of thermodynamics may shed much light on the mysterious Kovtun-Son-Starinets (KSS) bound on the ratio of viscosity to entropy density. In particular, we obtain the lower bound $η/s +O(η^3/s^3)\geq 1/4π$. Furthermore, for conformal field theories we obtain a new fundamental bound on the value of the relaxation coefficient $τ_π$ of causal hydrodynamics, which has been the focus of much recent attention: $(τ_πT)^2\geq {{(\sqrt{3}-1)}/{2π^2}}$.

4 pages