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Temperatures in Grains and Plasma

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.