# 统计物理短评集

1. 相变是热力学函数在热力学极限下的奇异性导致的。不同的奇异性划分了不同类型的相变。一般而言，称一级相变和连续相变(高阶导数的不连续)。为什么在统计力学中不再按照艾伦菲斯特(Ehrenfest)的分类称呼高级相变，而是采取连续相变呢？这是因为艾伦菲斯特按照自由能导数不连续的分类在相变理论的发展中被证明是错误的。在他的年代，尚不知道在连续相变点的非解析性不仅仅是导数的不连续，而是比热等热力学量的发散。在统计力学中，对于发散的处理导致了研究连续相变的临界现象理论。因此，现在一般说D维相图上自由能的解析区域定义了，存在不同维度Ds的不解析处，共维度(D-Ds)1的地方定义了相边界。自由能在所有相图上均连续，那么，通过相边界发生相变时，只有两种可能的不解析性。一是在相边界一级导数不连续，带来了潜热，是一级相变。二是在相边界所有自由能一级导数都连续，没有潜热，是连续相变，连续相变联系着发散带来的临界现象。

2. 传统热力学意义下的相变是可基于能熵平衡(Energy-entropy balance)判断而发生于一个有限温度的有序化。波色-爱因斯坦凝聚(BEC)则发生在绝对零度附近，因为热能接近零或远小于原子激发能量而没有热能激发，因此体系所有原子凝聚于基态，称BEC。量子相变有很多，但是有本质区别，取决于量子性在相变点具体的作用。例如超流，虽是BEC, 但是却可以用朗道相变理论描述，这是因为临界点关联长度统治的原因。零温下，调节哈密尔顿量中的(非温度)参数导致的相变是量子相变; 非零温，热涨落导致的相变是传统可用朗道理论描述的相变。放松一点，相变量子与否取决于热能和量子特征能量的大小比。在此意义下，超流相变不是量子相变，因为其发生于有限温度，在临界点，由于关联长度发散及临界慢化，导致kTc>hw，是热涨落相变，可用朗道理论描写，而其量子性仅仅体现于序参量是由量子性导致的序。

The long range, attractive part of LJ potential corresponds to the so-called non-retarded vdw force, where, due to the relatively "short" interaction range, one needs not to consider the non-instantaneous or local feature of interaction (i.e. relativity effect). This part actually is responsible for the b parameter in vdw equation and triggers the Gas-Liquid transition. Further increasing distance between molecules, however, requires to take into account the relativity effect and this calculation was done by Casimir and Polder, which is called Casimir-Polder force between molecules, corresponding to retarded inter-molecule interaction. Then Casimir switched the way of thinking, namely, instead of thinking the quantum fluctuation of interacting objects, he, motivated by Bohr, focused on the background (vacuum) fluctuation, this line of re-thinking led to the famous Casimir force, which is for interaction between macrobodies and thereby relativity is included naturally due to macro-length invovled. This long range feature of Casimir force also results in the universality feature because short range, fast processes have been averageed out. Afterwards, E. M. Lifshitz and collaborators generalized the Casimir calculation into the interaction between macro dielectric media, basing their calculation on the fluctuation-dissipation theorem.

https://blog.sciencenet.cn/blog-2438753-1297103.html

## 全部精选博文导读

GMT+8, 2022-1-23 13:12