Nonequilibrium Statistical Mechanics for Adiabatic Piston Problem

作者：Itami Masato^*; Sasa Shin ichi

来源：Journal of Statistical Physics, 2015, 158(1): 37-56.

DOI：10.1007/s10955-014-1115-7

• Adiabatic piston problem
• Master Boltzmann equation
• Stochastic energetics
• Local detailed balance condition
• Linear response theory

We consider the dynamics of a freely movable wall of mass M with one degree of freedom that separates a long tube into two regions, each of which is filled with rarefied gas particles of mass m. The gases are initially prepared at equal pressure but different temperatures, and we assume that the pressure and temperature of gas particles before colliding with the wall are kept constant over time in each region. We elucidate the energetics of the setup on the basis of the local detailed balance condition, and then derive the expression for the heat transferred from each gas to the wall. Furthermore, by using the condition, we obtain the linear response formula for the steady velocity of the wall and steady energy flux through the wall. By using perturbation expansion in a small parameter epsilon = root m/M, we calculate the steady velocity up to order epsilon.

• 出版日期2015-1