Temperatures in Grains and Plasma

TL;DR

This paper argues that granular media are better modeled with two temperatures, one for grains and one for atoms, similar to plasma, providing new insights into their thermodynamic behavior.

Contribution

It introduces the analogy between grains and plasma, emphasizing the importance of two temperatures and their nonlinear energy dependence for understanding granular media.

Findings

Two-temperature plasma analogy offers better insight into grains.

Energy in plasma depends quadratically on temperature difference.

Irreversible collisions drive temperature equilibration in both systems.

Abstract

Grains are widely assumed to be characterized by a single temperature -- derived either from the configurational entropy, or employing the kinetic theory. Yet granular media do have two temperatures, $T_g$ and $T$, pertaining to the grains and atoms. It is argued here that a two-temperature plasma yields a more useful analogy for grains than a molecular gas: (1)~Irreversible collisions also occur in plasma, to reach the equilibrium of equal temperature. (2)~The plasma energy is not linear in the two temperatures; it is quadratic in the temperature difference, minimal at equilibrium. Both points have valid analogues in grains, yielding useful insights.