现代统计力学和热力学新世代的统计力学三大定理

美国归侨冯向军博士，2017年8月15日写于美丽故乡

【摘要】牛顿第一定律强调：在无任何外力作用下，直线上的质点将保持匀速直线运动。牛顿第二定律指出力是加速度或非均匀速度的原因。牛顿第三定律则揭示：对于每一种作用，存在与之相等的反作用。与牛顿三大定律相对应，现代统计力学和热力学新世代有统计力学三大定理。

【现代统计力学和热力学新世代的统计力学第一定理】

 在无任何非自然约束条件下，一切分布以最大发生概率成为均匀分布。

【现代统计力学和热力学新世代的统计力学第二定理】

 除自然约束条件以外的与因果律相符合的约束条件，是非均匀分布产生的原因。与因果律相符合的约束条件包括而不限于：

（1）自洽约束条件：若欲成就的“果”分布为f(xi)，则“因”分布pi 服从：pi = f(xi),i = 1，2，...,n 和

p1/f(x1) + p2/f(x2) + ... + pn/f(xn) = 常数n （1-1)  

（2）广义的克劳修斯熵等于广义的玻尔兹曼熵:

-log(f(x)/a) = log(W) （1-2）

这其中W是欲成就的非均匀分布f(x)所对应的微观状态总数，a是f(x)的分布系数。

广义的克劳修斯熵 = -log(f(x)/a) (1-3)

广义的玻尔兹曼熵 = log(W) （1-4）    

（3）变量间隔x内给定事件出现总数的统计平均值Freq的分布等于变量间隔x后给定事件才出现的概率分布f(x)的信息量。

Freq = -log(f(x)) (1-5)

【现代统计力学和热力学新世代的统计力学第三定理】

在无任何非自然约束条件下，任何存在A都在时间和空间等存在的形式上，与其对立面非A平等地合一：平等的A与非A以最大发生概率同时空发生。

 以上现代统计力学和热力学新世代的统计力学三大定理之所以被称为定理，那是因为这三大定理均有数学证明。

 对于概率分布p1，p2，...，pn，上述发生概率P有确切定义：

P = p1 * p2 *...* pn (1-6)

牛顿运动定律的英文版原文

第一定律

I. Every object in a state of uniform motion tends to remain in that state o

f motion unless an external force is applied to it.

第二定律

II. The relationship between an object's mass m, its acceleration a, and the

applied force F is F = ma. Acceleration and force are vectors (as indicate

d by their symbols being displayed in slant bold font); in this law the dire

ction of the force vector is the same as the direction of the acceleration ve

ctor.

第三定律

III. For every action there is an equal and opposite reaction.

牛顿运动定律的英文版原文

第一定律

I. Every object in a state of uniform motion tends to remain in that state o

f motion unless an external force is applied to it.

第二定律

II. The relationship between an object's mass m, its acceleration a, and the

applied force F is F = ma. Acceleration and force are vectors (as indicate

d by their symbols being displayed in slant bold font); in this law the dire

ction of the force vector is the same as the direction of the acceleration ve

ctor.

第三定律

III. For every action there is an equal and opposite reaction.

牛顿运动定律的英文版原文

第一定律

I. Every object in a state of uniform motion tends to remain in that state o

f motion unless an external force is applied to it.

第二定律

II. The relationship between an object's mass m, its acceleration a, and the

applied force F is F = ma. Acceleration and force are vectors (as indicate

d by their symbols being displayed in slant bold font); in this law the dire

ction of the force vector is the same as the direction of the acceleration ve

ctor.

第三定律

III. For every action there is an equal and opposite reaction.