  The 1970 paper, "Decay of the Velocity Correlation Function" [Phys. Rev. A1,
18 (1970), see also Phys. Rev. Lett. 18, 988 (1967)] by Berni Alder and Tom
Wainwright, demonstrated, by means of computer simulations, that the velocity
autocorrelation function for a particle in a gas of hard disks decays
algebraically in time as $t^{-1},$ and as $t^{-3/2}$ for a gas of hard spheres.
These decays appear in non-equilibrium fluids and have no counterpart in fluids
in thermodynamic equilibrium. The work of Alder and Wainwright stimulated
theorists to find explanations for these "long time tails" using kinetic theory
or a mesoscopic mode-coupling theory. This paper has had a profound influence
on our understanding of the non-equilibrium properties of fluid systems. Here
we discuss the kinetic origins of the long time tails, the microscopic
foundations of mode-coupling theory, and the implications of these results for
the physics of fluids. We also mention applications of the long time tails and
mode-coupling theory to other, seemingly unrelated, fields of physics. We are
honored to dedicate this short review to Berni Alder on the occasion of his
90th birthday!
