广义极值原理及其与最小值、最大值原理的联系和统一

THE GENERALIZED EXTREMUM PRINCIPLE AND ITS RELATIONSHIP AND UNITY WITH THE PRINCIPLE OF MINIMUM OR MAXIMUM

本文将热力学中的熵产生推广到任意的物理系统,即任意系统的广义熵产生是其广义力和广义流的乘积.还定义了系统运动的广义位形空间,并引进一个依赖于体系在广义位形空间中的广义运动路径(推广的广义熵产生)的广义作用量,运用泛函极值条件得出广义极值原理:“在一定条件下,系统状态在经过广义位形空间两点的一切可能运动中,真实运动使广义作用量取极值.如果广义作用量的二阶变分大于零,则取最小值;反之取最大值。”由上原理出发,可分别得出最小作用量原理,哈密顿原理、费马原理、H定理和最小熵产生原理。得出各个最小值、最大值原理是广义极值原理的特例结论,从而将各个最小值、最大值原理统一成为广泛的广义极值原理。

In this paper the Produced-entropy of thermodynamics is being popularized to a arbitrary physical system. Generalized Produced-entropy is the product of General Force and General Flow. A Generalized Displacement-space has been defined, And a Generalized Act-capacity of system is being introduced which is dependent on the generalized moving way (popularized Generalized Pro-duced-entropy) in the Generalized Displacement- space. A Generalized Extremum Principle have been obtained by use of the functional extremum conditions: 'on certain conditions, the real move of system state will make Generalized Act-capacity to get extreme value in all passible move of it throughing arbitrary two points of the Generalized Displacement- space, if the quadratic variation of the Generalized Act-capacity is larger than zero, it is minimum value, conversely, it is maximum value'. From the generalized principle, we can derive Least-Action Principle, Hamiltion Principle, H Theorem, Least Entropy-produced Principle and so on. A conclusion is reached that all Minimum or Maximum Principles are special case of the Generalized Extremeum principle. Thus all Minimum or Maximum Prnciples have been unified as the Generalized Extremum Principle.