One-Dimensional Gases with Hard-Core Repulsion

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Abstract
An elementary mathematical device previously employed to derive the statistical mechanical properties of a classical one‐dimensional gas with interaction potential that satisfies a linear differential equation with constant coefficients over the domain (0, ∞) is shown to be also applicable when the potential contains a repulsive hard core. In particular, the thermodynamic properties of a one‐dimensional plasma of hard rods and of the gas model of Kac are derived. The infinite‐range phase transition obtained in the latter case by Kac, Uhlenbeck, and Hemmer is found to be amenable to investigation by the methods used.