From Thermodynamics to the Bound on Viscosity

TL;DR

This paper explores how the generalized second law of thermodynamics can provide insights into the Kovtun-Son-Starinets bound on viscosity to entropy density ratio and introduces a new fundamental bound on the relaxation coefficient in conformal field theories.

Contribution

It links thermodynamic principles to bounds on physical quantities in quantum field theories, offering new theoretical limits on viscosity and relaxation coefficients.

Findings

Derived a lower bound on η/s consistent with the KSS bound.

Established a new fundamental bound on the relaxation coefficient τ_π.

Connected thermodynamics with hydrodynamic bounds in conformal field theories.

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 $\eta/s +O(\eta^3/s^3)\geq 1/4\pi$. 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: $(\tau_{\pi}T)^2\geq {{(\sqrt{3}-1)}/{2\pi^2}}$.