This is an abstract and powerful mathematical statement of the first law of thermodynamics.
这是热力学第一定律的一个抽象,而且具有很强数学性的表述。
I'll show those again, but what I want to do mostly today is try to put a mathematical statement of the second law in place that corresponds to the verbal statements that we saw last time.
今天我还将跟你们讲这些,但今天的重点是,对上次口头表述内容中的热力学,第二定律,的数学推导,我们上次看到的。
The way the physics works is you will find some laws of motion in mathematical form, you put in the initial conditions of whatever, you solve the equations, and the answer that comes, you have no choice.
在物理问题中,你可以用数学方法得到运动定律,你代入初始条件,然后解方程,获得答案,你别无选择
People have done experiments through the ages, and they've accumulated the knowledge from these experiments, and they've synthesized these experiments into a few basic empirical rules, empirical laws, which are the laws of thermodynamics.
很长的时期内,人们做了大量的实验,从这些实验中积累知识,将这些实验总结成一些基本的经验法则和定律,这就是热力学的定律,然后,人们给这些定律添加,数学架构。
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