 |
How many ways can you distribute 9 units of energy among 6 identical particles?
将9个单位的能量分配给6个相同的粒子，有多少种方法？
The three distributions of particles at left each have the same energy, the same kind of particles, and the same number of particles, yet the distribution at the right is 30 times more likely than the one at the left. Why is this? For the distinguishable particles which are presumed by the Maxwell-Boltzmann distribution, it matters not only how many particles are in each state, but which particles are in each state.
左边的三个粒子分布具有相同的能量、相同的粒子种类和相同的粒子数目，然而右边的分布比左边的分布更可能30倍。为什么会出现这种情况？对于被麦克斯韦-玻尔兹曼分布所假设的可区分粒子来说，不仅粒子在每个状态中的数量重要，粒子在每个状态中的具体身份也至关重要。
|
Blatt uses the term "macrostate" to describe the characterization of the system which gives just the number of particles in each state; the diagram above shows three of the 26 possible macrostates for this system. The term "microstate" is used for the more detailed characterization in which the specific energy level for each particle is given. The macrostate at left has only 6 microstates, because there are only 6 ways to put one particle in level 9 and the other 5 in level 0. But there are 180 ways to achieve the macrostate at right, so if every distribution is presumed to be equally likely, then the system is 30 times more likely to be found in the right hand macrostate.
Blatt使用“宏观态”一词来描述系统的一个特征，即仅给出每个态中粒子的数量；上图显示了该系统26种可能的宏观态中的三种。“微观态”一词用于更详细的描述，其中每个粒子的具体能级都被指定。左边的宏观态只有6个微观态，因为只有一种方式将一个粒子放在第9级，其余5个放在第0级。但右边的宏观态有180种实现方式，所以如果假设每种分布都等概率，则系统更可能处于右边的宏观态，可能性是30倍。
The number of distinguishable ways to produce each distribution is given by
产生每种分布的可区分方式数目由以下公式给出
So for the three macrostates pictured above, the numbers of microstates are
对于上面所示的三个宏观状态，微观状态的数量是
(Recall that 0!=1 so that the unoccupied states do not affect the calculation.)
（注意0!=1，因此未被占据的状态不影响计算。）
Now to establish the distribution function for the number of particles in each energy state, the number of particles in each state must be averaged over all of the microstates. For each macrostate, the number of particles in a given energy level is multiplied by the number of microstates. The sum of those products is divided by the total number of microstates, which is 2002 in this case.
现在要建立每个能级中粒子数的分布函数，每个状态中的粒子数必须在所有微态上进行平均。对于每个宏观态，给定能级中的粒子数乘以微态数目。这些乘积之和除以总微态数目，这里是2002。
The number of microstates (the multiplicity W) for q units of energy among N equally probable states can be mathematically evaluated from the expression
q单位的能量在N个等概率状态中分配时的微观状态数（即简并度W）可以从表达式数学地计算得出
which for this case becomes
在本例中变为
|
