2007/10/31 by Itzhak Fouxon, Gerold Betschart, Jacob D. Bekenstein · 5 citations
Engineering · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Fluid Dynamics and Turbulent Flows #gr-qc #hep-th #physics.flu-dyn
paper · pdf · doi:10.1103/physrevd.77.024016
published as Phys.Rev.D77:024016,2008 · 11 pages, 1 figure, published version
openalex publication_date 2008/01/10 · arxiv created 2008/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe a new paradox for ideal fluids. It arises in the accretion of an 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 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.