更改

由于自由度是独立的，因此系统的内部能量等于每个自由度相关的平均能量之和，由此得到了结果。

由于自由度是独立的，因此系统的内部能量等于每个自由度相关的平均能量之和，由此得到了结果。

==Generalizations==

== Generalizations 概括 ==

The description of a system's state as a [[point (geometry)|point]] in its phase space, although mathematically convenient, is thought to be fundamentally inaccurate. In [[quantum mechanics]], the motion degrees of freedom are superseded with the concept of [[wave function]], and [[operator (physics)|operators]] which correspond to other degrees of freedom have [[point spectrum|discrete spectra]]. For example, [[angular momentum operator#Spin, orbital, and total angular momentum|intrinsic angular momentum]] operator (which corresponds to the rotational freedom) for an [[electron]] or [[photon]] has only two [[eigenvalue]]s. This discreteness becomes apparent when [[action (physics)|action]] has an [[order of magnitude]] of the [[Planck constant]], and individual degrees of freedom can be distinguished.

The description of a system's state as a [[point (geometry)|point]] in its phase space, although mathematically convenient, is thought to be fundamentally inaccurate. In [[quantum mechanics]], the motion degrees of freedom are superseded with the concept of [[wave function]], and [[operator (physics)|operators]] which correspond to other degrees of freedom have [[point spectrum|discrete spectra]]. For example, [[angular momentum operator#Spin, orbital, and total angular momentum|intrinsic angular momentum]] operator (which corresponds to the rotational freedom) for an [[electron]] or [[photon]] has only two [[eigenvalue]]s. This discreteness becomes apparent when [[action (physics)|action]] has an [[order of magnitude]] of the [[Planck constant]], and individual degrees of freedom can be distinguished.