A semiclassical approach to \eta/s bound through holography

Abstract

We consider the holographic principle, in its lightsheet formulation, in the semiclassical context of statistical-mechanical systems in classical Einstein spacetimes. A local condition, in terms of entropy and energy local densities of the material medium under consideration, is discussed, which turns out to be necessary and sufficient for the validity of the closely-related generalized covariant entropy bound. This condition is apparently a general consequence or expression of flat-spacetime quantum mechanics alone, without any reference to gravity. Using it, a lower bound \eta/s >= 1/4\pi can be derived, with the limit attained (in certain circumstances) by systems hydrodynamically dominated by radiation quanta.