中子输运的随机理论

运用概率理论,考虑t时刻n个相空间点(r,uiΩi)单位体元中分别出现Ni(i=1,2,…,n)个中子的概率PN(r,t,uΩ),提出一个新的中子输运的随机理论,导出概率母函数Fn的非线性积分微分方程组。在某些近似下,n=1概率分布一阶矩方程恰好是中子平均数玻尔兹曼方程。将各向同性散射的单速中子随机理论应用于点堆模型。在一个超临界系统中,当t→∞时,出现有限个中子的概率为零,PN=0(0<N<∞),即系统内或没有中子,或有无限多中子。给出了母函数的近似解,导出了母函数概率分布各阶矩的近似方程及解式。标准差公式表明,当初始中子数起伏ξ0较大,初始中子平均数N0不够多,或中子源强Q很弱时,对于0<λ1的增殖系统,中子数的起伏很大,应予以重视。

Entropy Production along Dominant Pathway of Nonequilibrium Phase Transition in Mesoscopic Chemical System

We consider a bistable mesoscopic chemical reaction system and calculate entropy produc- tion along the dominant pathway during nonequilibrium phase transition. Using probability generating function method and eikonal approximation, we first convert the chemical master equation into the classical Hamilton-Jacobi equation, and then find the dominant pathways between two steady states in the phase space by calculating zero-energy trajectories. We find that entropy productions are related to the actions of the forward and backward dominant pathways. At the coexistence point where the stabilities of the two steady states are equiv alent, both the system entropy change and the medium entropy change are zero; whereas at non-coexistence point both of them are nonzero.