Mathematical study of Streater's model on Brownian particle gas. II

We continue to study Streater's model on Brownian particle gas in statistical mechanics on bounded domains in ${\bf R}^n$. If $n\leq 2$ and the entropy production is bounded, there is an a priori estimate of the solution global in time. Under additional properties on entropy and entropy production, this solution converges to a unique steady state, strongly and weakly for the models on classical and quantum particles, respectively.