What controls the relaxation time? Lessons learnt from simple liquids' quasiuniversality

The relaxation time of a supercooled liquid is extremely temperature and density dependent, approaching hours upon cooling or compression. Is this quantity controlled by the entropy, is it controlled by high-frequency elastic properties as assumed in the shoving and related elastic models, or by another physical property? It is far from certain that there is a simple and generally valid answer to this question for glass-forming liquids with quite different chemistry, but as physicists we like to think that this is the case. The talk summarizes recent results [1] on the quasiuniversality of simple liquids, where a simple liquid is defined as a system with strong virial / potential-energy correlations in the equilibrium NVT fluctuations. Such systems, which include e.g. the Lennard-Jones liquid, have good isomorphs. An isomorph is a curve in the phase diagram along which structure, dynamics, and some thermodynamic properties in reduced units are invariant to a good approximation [2-5]. It was recently conjectured [1] that simple liquids have almost the same isomorphs in the sense that these systems are characterized by a quasiuniversal one-parameter family of reduced-coordinate constant-potential-energy manifolds encoding all isomorph invariants. The entropy is the logarithm of the area of this manifold and the high-frequency elastic properties are basically the surface's curvature. Since the relaxation time is also encoded in the manifold, both quantities will appear to ``control'' the relaxation time, as will any isomorph invariant.\\[4pt] References: [1] J. C. Dyre, arXiv:1208.1748 (2012).\\[0pt] [2] N. Gnan et al., J. Chem. Phys. 131, 234504 (2009).\\[0pt] [3] N. Gnan et al., Phys. Rev. Lett. 104, 125902 (2010).\\[0pt] [4] U. R. Pedersen et al., Phys. Rev. Lett. 105, 157801 (2010).\\[0pt] [5] T. Ingebrigtsen et al., Phys. Rev. X 2, 011011 (2012).