The bound on viscosity and the generalized second law of thermodynamics

TL;DR

This paper explores a paradox involving ideal fluids and black holes that challenges the generalized second law of thermodynamics, leading to bounds on fluid viscosity and correlation length based on thermodynamic principles.

Contribution

It introduces a new paradox for ideal fluids near black holes and derives bounds on viscosity and correlation length from the generalized second law of thermodynamics.

Findings

A paradox for ideal fluids violating the second law near black holes.

Lower bounds on fluid correlation length based on entropy bounds.

Viscosity is bounded from below, related to the KSS bound.

Abstract

We describe a new paradox for ideal fluids. It arises in the accretion of an \textit{ideal} fluid onto a black hole, where, under suitable boundary conditions, the flow can violate the generalized second law of thermodynamics. The paradox indicates that there is in fact a lower bound to the correlation length of any \textit{real} fluid, the value of which is determined by the thermodynamic properties of that fluid. We observe that the universal bound on entropy, itself suggested by the generalized second law, puts a lower bound on the correlation length of any fluid in terms of its specific entropy. With the help of a new, efficient estimate for the viscosity of liquids, we argue that this also means that viscosity is bounded from below in a way reminiscent of the conjectured Kovtun-Son-Starinets lower bound on the ratio of viscosity to entropy density. We conclude that much light may be shed on the Kovtun-Son-Starinets bound by suitable arguments based on the generalized second law.