Seguin Brian, Fried Eliot
Department of Mathematics and Statistics, 805 Sherbrooke Street West, Montreal, QC H3A 2K6, Tel.: 514-398-2998, ,
Arch Ration Mech Anal. 2013 Jan 1;207(1):1-37. doi: 10.1007/s00205-012-0551-2.
Working on a state space determined by considering a discrete system of rigid rods, we use nonequilibrium statistical mechanics to derive macroscopic balance laws for liquid crystals. A probability function that satisfies the Liouville equation serves as the starting point for deriving each macroscopic balance. The terms appearing in the derived balances are interpreted as expected values and explicit formulas for these terms are obtained. Among the list of derived balances appear two, the tensor moment of inertia balance and the mesofluctuation balance, that are not standard in previously proposed macroscopic theories for liquid crystals but which have precedents in other theories for structured media.
在考虑由离散刚体杆系统确定的状态空间的基础上，我们运用非平衡统计力学来推导液晶的宏观平衡定律。满足刘维尔方程的概率函数作为推导每个宏观平衡的起点。推导平衡中出现的项被解释为期望值，并得到了这些项的显式公式。在推导的平衡列表中出现了两个平衡，即张量惯性矩平衡和介观涨落平衡，这在先前提出的液晶宏观理论中并不标准，但在其他结构化介质理论中有先例。
