Proposed lower bound for the shear viscosity to entropy density ratio in some dense liquids

Starting from relativistic quantum field theories, Kovtun et al. (2005) have quite recently proposed a lower bound η/s⩾ℏ/(4πkB)η/s⩾ℏ/(4πkB), where η is the shear viscosity and s the volume density of entropy for dense liquids. If their proposal can eventually be proved, then this would provide key theoretical underpinning to earlier semiempirical proposals on the relation between a transport coefficient η and a thermodynamic quantity s  . Here, we examine largely experimental data on some dense liquids, the insulators nitrogen, water, and ammonia, plus the alkali metals, where the shear viscosity η(T)η(T) for the four heaviest alkalis is known to scale onto an ‘almost universal’ curve, following the work of Tankeshwar and March a decade ago. So far, all known results for both insulating and metallic dense liquids correctly exceed the lower bound prediction of Kovtun et al.