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 $\eta /s+O({\eta }^3/s^3)\ge 1/4\pi$. Furthermore, for conformal field theories we obtain a new fundamental bound on the value of the relaxation coefficient ${\tau }_{\pi }$ of causal hydrodynamics, which has been the focus of much recent attention: $({\tau }_{\pi }T{)}^2\ge (\sqrt{3}-1)/2{\pi }^2$.

4 pages

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Cited by in corpus (1)

• Hydrodynamics of strongly coupled non-conformal fluids from gauge/gravity duality