Analytical probability solution and phase transition of a two-dimensional few-body adiabatic piston system

¹ Department of Physics, Beijing Normal University - Beijing 100875, PRC
² China Center for Advanced Science and Technology (CCAST) (World Laboratory) P.O. Box 8730, Beijing 100080, PRC
³ The Key Laboratory of Beam Technology and Material Modification of the Ministry of Education, Beijing Normal University - Beijing 100875, PRC

Corresponding author: ganghu@bnu.edu.cn

Received: 23 February 2004
Accepted: 26 May 2004

Abstract

The spatial probability distribution of a few-body “adiabatic piston” system in a two-dimensional box is analytically computed in statistical equilibrium state, and the explicit solution of the probability distribution of the piston is obtained. The realization of the microcanonical equilibrium state of the system is justified by the agreement between the theoretical predictions and numerical observations. An interesting transition from unimodal probability distribution phase to a multi-peak distribution phase is analytically predicted, and fully confirmed by numerical simulations. This transition can be regarded as one of the primary prototypes of few-body phase transitions.