  Building on the elastically collective nonlinear Langevin equation theory
developed for hard spheres in the preceding paper I, we propose and implement a
quasi-universal theory for the alpha relaxation of thermal liquids based on
mapping them to an effective hard sphere fluid via the dimensionless
compressibility. The result is a zero adjustable parameter theory that can
quantitatively address in a unified manner the alpha relaxation time over 14 or
more decades. The theory has no singularities above zero Kelvin, and relaxation
in the equilibrium low temperature limit is predicted to be of a roughly
Arrhenius form. The two-barrier (local cage and long range collective elastic)
description results in a rich dynamic behavior including apparent Arrhenius,
narrow crossover and deeply supercooled regimes, and multiple characteristic or
crossover times and temperatures of clear physical meaning. Application of the
theory to nonpolar molecules, alcohols, rare gases and liquids metals is
carried out. Overall, the agreement with experiment is quite good for the
temperature dependence of the alpha time, plateau shear modulus and Boson-like
peak frequency for van der Waals liquids, though less so for hydrogen-bonding
molecules. The theory predicts multiple growing length scales upon cooling,
which reflect distinct aspects of the coupled local hopping and cooperative
elastic physics. Calculations of an activation volume that grows with cooling,
which is correlated with a measure of dynamic cooperativity, agree
quantitatively with experiment. Comparisons with elastic, entropy crisis,
dynamic facilitation and other approaches are performed, and a fundamental
basis for empirically-extracted crossover temperatures is established. The
present work sets the stage for addressing distinctive glassy phenomena in
polymer melts, and diverse liquids under strong confinement.
