线性不可逆过程的协同效应分析  

Research on the Synergistic Effect of Linear Thermodynamics of Irreversible Processes

作　　者：王永岩[1] 苏传奇[1] 位文斌[1] 

机构地区：[1]青岛科技大学机电工程学院,山东青岛266061

出　　处：《数学的实践与认识》2013年第2期170-176,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(50974077,51074094)

摘　　要：利用矩阵理论对线性不可逆过程的协同效应进行了分析.与向量空间相类比,定义了热力学流空间中的内积以及协同系数.协同系数的大小反映了两个不可逆过程间的协同程度.由唯象系数矩阵引出了协同矩阵与协同系数矩阵.对于导热不可逆过程,协同矩阵所对应的二次型是耗散函数.对于孤立体系,证明了协同矩阵所对应的二次型对时间的导数为负值,它可以作为体系的一个李雅普诺夫函数.By the use of matrix theory the synergistic effect of linear thermodynamics of irreversible processes is analyzed. By analogy to the vector space, the inner product of ther- modynamic flux space and synergistic coefficient is defined. Synergistic coefficient is the re- flection of synergy degree of two irreversible processes. The synergistic matrix and synergistic coefficient matrix are derived from the phenomenological coefficient matrix. The quadratic form of synergistic matrix corresponding to heat conduction process is dissipation function. For the isolated system, the derivative with respect to time of quadratic form of synergistic matrix is negative.So the quadratic form of synergistic matrix can be regarded as a Lyapunov function of the system.

关 键 词：线性不可逆过程热力学 协同系数 协同矩阵 耗散函数 

分 类 号：O151.21[理学—数学] O414.1[理学—基础数学]