Abstract
The spatial probability distribution of a few-body “adiabaticpiston” system in a two-dimensional box is analytically computedin statistical equilibrium state, and the explicit solution ofthe probability distribution of the piston is obtained. Therealization of the microcanonical equilibrium state of thesystem is justified by the agreement between the theoreticalpredictions and numerical observations. An interesting transitionfrom unimodal probability distribution phase to a multi-peakdistribution phase is analytically predicted, and fully confirmedby numerical simulations. This transition can be regarded as oneof the primary prototypes of few-body phase transitions.
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