Why Non-equilibrium is Different

TL;DR

This paper reviews the non-equilibrium long time tail phenomena in fluid systems, discussing their kinetic origins, theoretical foundations, and broader implications across physics fields.

Contribution

It provides a comprehensive overview of the microscopic and theoretical understanding of long time tails in non-equilibrium fluids, highlighting their significance and applications.

Findings

Velocity autocorrelation functions decay algebraically in non-equilibrium fluids.

Mode-coupling theory explains long time tail origins.

Implications extend to various physics fields.

Abstract

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!