  We present an analysis and discuss consequences of the strong correlations of
the configurational parts of pressure and energy in their equilibrium
fluctuations at fixed volume reported for simulations of several liquids in the
companion paper [arXiv:0807.0550]. The analysis concentrates specifically on
the single-component Lennard-Jones system. We demonstrate that the potential
may be replaced, at fixed volume, by an effective power-law, but not because
only short distance encounters dominate the fluctuations. Indeed, contributions
to the fluctuations are associated with the whole first peak of the RDF, as we
demonstrate by an analysis of the spatially resolved covariance matrix. The
reason the effective power-law works so well depends on going beyond
single-pair effects and on the constraint of fixed volume. In particular, a
better approximation to the potential includes a linear term, which contributes
to the mean values of potential energy and virial, but not to their
fluctuations. We also study the T=0 limit of the crystalline phase, where the
correlation coefficient becomes very close, but not equal, to unity. We then
consider four consequences of strong pressure-energy correlations: (1)
analyzing experimental data for supercritical Ar we find 96% correlation; (2)
we discuss the significance acquired by the correlations for viscous van der
Waals liquids approaching the glass transition: For strongly correlating
viscous liquids knowledge of just one of the eight frequency-dependent
thermoviscoelastic response functions basically implies knowledge of them all;
(3) we re-interpret aging simulations of ortho-terphenyl carried out by Mossa
{\it et al.} in 2002, showing their conclusions follow from the strongly
correlating property; and (4) we discuss correlations in model biomembranes.
