Minimal quantum viscosity from fundamental physical constants

Abstract

Viscosity of fluids is strongly system-dependent, varies across many orders of magnitude and depends on molecular interactions and structure in a complex way not amenable to first-principles theories. Despite the variations and theoretical difficulties, we find a new quantity setting the minimal kinematic viscosity of fluids: $\nu_m=\frac{1}{4\pi}\frac{\hbar}{\sqrt{m_em}}$, where $m_e$ and $m$ are electron and molecule masses. We subsequently introduce a new property, the "elementary" viscosity $\iota$ with the lower bound set by fundamental physical constants and notably involving the proton-to-electron mass ratio: $\iota_m=\frac{\hbar}{4\pi}\left({\frac{m_p}{m_e}}\right)^{\frac{1}{2}}$, where $m_p$ is the proton mass. We discuss the connection of our result to the bound found by Kovtun, Son and Starinets in strongly-interacting field theories.