The bound on viscosity and the generalized second law of thermodynamics

Details The bound on viscosity and the generalized second law of thermodynamics The bound on viscosity and the generalized second law of thermodynamics

2007-10-07

arxiv.org/abs/0710.1429v2

Phys.Rev.D77:024016,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

11 pages, 1 figure, published version

Scientific paper

10.1103/PhysRevD.77.024016

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.

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