Correlation Length in a Nonequilibrium Gas

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Abstract
We demonstrate on a gas model that, if three‐body events are neglected, the nonequilibrium correlations extend over a distance proportional to the relaxation time of the one‐body distribution function. For homogeneous perturbations this correlation length is the mean free path, the relaxation time being the mean free flight time. In the hydrodynamical limit both the relaxation time of nonhomogeneous perturbations and the correlation length become infinite. This resolves the apparent contradistinction between the recent claim of a finite correlation length for nonequilibrium (but homogeneous) gases and the occurrence of correlations with an infinite range leading to divergences in the virial expansion of transport coefficients which precisely describe hydrodynamical perturbations.