  Starting from relativistic quantum field theories, Kovtun et al. (2005) have
quite recently proposed a lower bound eta/s >= hbar /(4 pi kB), where eta 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 eta 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
eta(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.
