A semiclassical approach to \eta/s bound through holography

TL;DR

This paper explores a semiclassical holographic approach to derive the universal lower bound on the shear viscosity to entropy density ratio (/s) in fluid systems, linking quantum mechanics, entropy bounds, and hydrodynamics.

Contribution

It introduces a local entropy-energy condition in semiclassical spacetime that leads to the /s bound, connecting quantum mechanics and holography without explicit gravity.

Findings

Derived /s  bound from a local entropy-energy condition.

Identified conditions under which the bound is saturated by radiation-dominated systems.

Linked the bound to flat-spacetime quantum mechanics and holographic principles.

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.