Gravitation, Thermodynamics, and the Bound on Viscosity

TL;DR

This paper explores the fundamental connection between gravity, quantum theory, and thermodynamics, providing insights into the universal lower bound on the shear viscosity to entropy density ratio in fluids via the AdS/CFT correspondence.

Contribution

It demonstrates that the viscosity bound arises naturally from the interplay of gravity, quantum mechanics, and thermodynamics, offering a theoretical foundation for the conjectured limit.

Findings

The viscosity bound is a consequence of gravity and thermodynamics principles.

The AdS/CFT correspondence predicts a universal viscosity to entropy ratio.

The paper provides a conceptual explanation for the viscosity bound without requiring a proof of its universal validity.

Abstract

The anti-de Sitter/conformal field theory (AdS/CFT) correspondence implies that small perturbations of a black hole correspond to small deviations from thermodynamic equilibrium in a dual field theory. For gauge theories with an Einstein gravity dual, the AdS/CFT correspondence predicts a universal value for the ratio of the shear viscosity to the entropy density, $\eta/s=1/4\pi$. It was conjectured recently that all fluids conform to the lower bound $\eta/s \geq 1/4\pi$. This {\it conjectured} bound has been the focus of much recent attention. However, despite the flurry of research in this field we still lack a proof for the general validity of the bound. In this essay we show that this mysterious bound is actually a direct outcome of the interplay between gravity, quantum theory, and thermodynamics.