http://bjzc.org/lib/9/gljx/ts009059.pdf
在P-T 投影面上，如图4.7 所示上述水平线就成一点了；在固定的
T(TC 以下)，从气态跨过汽化线进入液态，熵会突变。而在C 点，它在图
4.9 中无水平线段，在该点既无体积的改变也无潜热，即熵是不变的或连
续的。熵在热力学中可以由一个自由能的热力学势对温度求一次导数而
得。这样，在C 点以下热力学势是连续的，但是它的一次导数有突变、
不连续，这就称为一阶相变。这个定义是1933 年厄伦弗斯给出的。一般
地，如果直至k-1 阶的热力学势导数连续，而第k 阶导数不连续，这样
的相变称为是k 阶相变。关于C 点是二阶相变点的结论，我们在下面会
看到
Questions
Top Recent
this video feels out of place...what does differentiable mean?
Abhi Pokhrel
A function is differentiable at a point when there's a defined derivative at that point. This means that the slope of the tangent line of the points from the left is approaching the same value as the slope of the tangent of the points from the right.
Still confused?
Think about this:
In all the examples he gave, the points where the functions weren't differentiable were where the function changed course. This means the speed it was going at completely changed. From the left side of the point, the function was going at one speed, but from the right side of the point, the function was going at a different speed. Since the function had different speeds from both sides, there was no defined speed at the point where the change happened. The function isn't differentiable at the point where the change happens.
铁磁的居里点)等。自然界中常见的只有这二种相变。
Still confused?
Think about this:
In all the examples he gave, the points where the functions weren't differentiable were where the function changed course. This means the speed it was going at completely changed. From the left side of the point, the function was going at one speed, but from the right side of the point, the function was going at a different speed. Since the function had different speeds from both sides, there was no defined speed at the point where the change happened. The function isn't differentiable at the point where the change happens.
朗道假设系统的自由能密度f 是磁矩密度的解析函数。在临界温度
附近，序参量——这里是磁矩密度M—应是一个很小的量，可以把f 展开
成M 的级数，且只保留到M 的四次方项。然后，根据系统的平衡态对应
于f 取极小，即可征明在临界点以上应有M=0，而在T＜TC 时M 不为0，
它满足M～(T －T)，或者说临界指数= 。
1
2 C b
朗道的二阶相变唯象理论看来十分简单，但它的物理含义是十分深
刻的。这里我们只是先谈一下用序参量对相变分类的意
义。按照序参量的描述，一阶相变的序参量有突变，而二阶相变的
序参量却是连续的。一阶相变的例子如非临界点处普通气液相变，外磁
场中的超导转变等。在那里热力学势连续而比热、磁化率或压缩率等不
连续。二阶相变的例子有前面提到的4He 在λ点的超流转变，没有外磁
场的超导转变点，气液相变的临界点处，以及许多磁相变的临界点处(如
铁磁的居里点)等。自然界中常见的只有这二种相变。
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