Multiplity for Energy Distribution

The evaluation of the number of ways you can distribute energy among a collection of particles or systems is important in physical calculations since any collection will tend toward the configuration of maximum multiplicity (maximum entropy).

评估将能量分配给一组粒子或系统的不同方式数目在物理计算中非常重要，因为任何一组系统都会倾向于最大多样性（最大熵）的配置。

The multiplicity Ω for q units of energy among N equally probable states is given by the expression:

q单位的能量在N个等概率状态中分配的简并度Ω由下式给出：

这有时也被称为系统的微观状态数。

Shroeder has a succinct way to demonstrate the above relationship. Suppose we use a dot to represent each of the q units of energy and a vertical line to denote the boundaries between the N states. An example of a distribution of q=8 units of energy in N=4 states would be

Shroeder 有一种简洁的方法来展示上述关系。假设用一个点来表示每个能量单位 q，用一条竖线表示 N 个状态之间的边界。一个 q=8 个能量单位分布在 N=4 个状态的例子就是

Now this can be seen as a distribution of two types of items, energy units and state boundaries. There would always be q units of energy and N-1 state boundaries for a total of q + N - 1 symbols. So the number of ways to distribute q units of energy would just be the combination

现在这可以看作是两种类型的物品的分布，即能量单位和状态边界。对于总共有 q + N - 1 个符号来说，总是有 q 个能量单位和 N-1 个状态边界。因此，将 q 个能量单位进行分布的方式数目 simply 就是组合数。

which is the number of ways you can pick q units of energy (the permutation) divided by the the number of ways to rearrange the q units of energy without changing the number in each state.

这是选取q单位能量的方法数（排列数）除以在不改变各态数量的情况下重新排列这些q单位能量的方法数。

Multiplicity for Energy Distribution