Phase Space

Statistics involves the counting of states, and the state of a classical particle is completely specified by the measurement of its position and momentum. If we know the six quantities

统计涉及对状态的计数，经典粒子的状态完全由其位置和动量的测量来确定。如果我们知道六个量

then we know its state. It is often convenient in statistics to imagine a six-dimensional space composed of the six position and momentum coordinates. It is conventionally called "phase space". The counting tasks can then be visualized in a geometrical framework where each point in phase space corresponds to a particular position and momentum. That is, each point in phase space represents a unique state of the particle. The state of a system of particles corresponds to a certain distribution of points in phase space.

然后我们就可以知道它的状态。在统计中，常常方便地想象出一个由六个位置和动量坐标组成的六维空间。它通常被称为“相空间”。这样，计数任务就可以在几何框架中可视化，其中相空间中的每一个点对应于特定的位置和动量。也就是说，相空间中的每一个点都代表粒子的一个独特状态。质点系的状态对应于相空间中某一点的分布。

The counting of the number of states available to a particle amounts to determining the available volume in phase space. One might preclude that for a continuous phase space, any finite volume would contain an infinite number of states. But the uncertainty principle tells us that we cannot simultaneously know both the position and momentum, so we cannot really say that a particle is at a mathematical point in phase space. So when we contemplate an element of "volume" in phase space

确定粒子可占据的状态数，相当于确定相空间中的可用体积。有人可能会认为，在连续的相空间中，任何有限的体积都将包含无限多个状态。但不确定性原理告诉我们，我们无法同时知道粒子的位置和动量，因此不能真正说一个粒子位于相空间中的一个数学点上。因此，当我们考虑相空间中的一个“体积”元素时，

then the smallest "cell" in phase space which we can consider is constrained by the uncertainty principle to be

然后，我们所能考虑的相空间中最小的‘电池’则受不确定性原理所限制

Phase Space: a Framework for Statistics