Basic theory and some applications concerning the ratio of shear viscosity to entropy density in dense fluids

Abstract

Much interest continues relating to the conjecture from string theory of an inequality satisfied by the ratio /s in dense fluids, where is the shear viscosity and s the entropy density. First, we summarise the models which have prompted the proposal of the inequality. Second, we consider a model equation of state which may be appropriate for the dense fluids NH 3 and H 2 O, both of which satisfy the inequality. Keywords: dense fluids; equation of state; string theory 1. Background and outlines In a recent study, the present authors have discussed, with examples of monatomic insulating liquids like argon, and metallic fluids, in particular the alkali metals [1] and the proposed lower bound for the ratio /s [2,3]. Here, denotes the shear viscosity, while s is the entropy density. Because of the continuing fundamental interest in this ratio, the present Letter begins by summarising recent fundamental theoretical predictions beyond those referred to in [1]. Then, following this, we shall consider a model equation of state going back to a proposal by Chapman and March [4], which we shall bring into contact with [1] in relation to results presented there for the number density versus temperature T under isobaric conditions for the dense fluids H 2 O and NH 3 . 2. Fundamental examples on ratio g/s: mainly from relativistic quantum field string theory methods In [1], we gave special attention to the theoretical study of Kovtun et al. [2] and also to that of Scha¨fer [3]. A very recent contribution by Evans and Threlfall [5] has provided some motivation for this further contribution on the ratio /s discussed at some length in [1]. Their work studies the thermal phase transition in a quantum-chromodynamics (QCD)