Information-Theoretic Derivation of a Nonequilibrium Velocity Distribution

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Abstract
In this paper we derive the velocity distribution for an ideal gas, using the information-theoretic point of view, and the assumption that one can selectively measure the properties of molecules moving in different directions. In the equilibrium case, this reduces to the usual "canonical" formalism, where the collisional invariants of mechanics exhaust our information. In the case of a heat flow, we are logically forced to a new, bimodal, probability distribution, whose behavior is determined by observables which are not constants of motion, in the sense of mechanics. This is the first instance, to our knowledge, where the information-theoretic point of view leads to new results, which are not obtainable by the classical approach. A simple experiment is proposed, to verify our results.

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