更改

In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.

In physics and chemistry, a degree of freedom is an independent physical parameter in the formal description of the state of a physical system. The set of all states of a system is known as the system's phase space, and the degrees of freedom of the system are the dimensions of the phase space.

在物理和化学领域中，''自由度''是对物理系统状态形式描述中的独立物理参数。系统所有状态的集合称为系统的'''<font color="#ff8000"> 相空间</font>'''，系统的自由度是相空间的维数。

在物理和化学领域中，'''<font color="#ff8000"> 自由度Degree of freedom</font>'''是对物理系统状态形式描述中的独立物理参数。系统所有状态的集合称为系统的'''<font color="#ff8000"> 相空间Phase space</font>'''，系统的自由度是相空间的维数。

In classical mechanics, the state of a point particle at any given time is often described with position and velocity coordinates in the Lagrangian formalism, or with position and momentum coordinates in the Hamiltonian formalism.

In classical mechanics, the state of a point particle at any given time is often described with position and velocity coordinates in the Lagrangian formalism, or with position and momentum coordinates in the Hamiltonian formalism.

在经典力学中，任何给定时间下'''<font color="#ff8000"> 质点</font>'''的状态，不同的力学形式会有不一样的描述，在拉格朗日力学中描述为位置和速度坐标，而在哈密顿力学中则描述为位置和动量坐标。

在经典力学中，任何给定时间下'''<font color="#ff8000"> 质点Point particle</font>'''的状态，不同的力学形式会有不一样的描述，在拉格朗日力学中描述为位置和速度坐标，而在哈密顿力学中则描述为位置和动量坐标。

In the 3D ideal chain model in chemistry, two angles are necessary to describe the orientation of each monomer.

In the 3D ideal chain model in chemistry, two angles are necessary to describe the orientation of each monomer.

在化学的三维'''<font color="#ff8000"> 理想链</font>'''模型中，描述每个单元结构方向的必要参数是它们的两个角度。

在化学的三维'''<font color="#ff8000"> 理想链Ideal chain</font>'''模型中，描述每个单元结构方向的必要参数是它们的两个角度。

Contrary to the classical equipartition theorem, at room temperature, the vibrational motion of molecules typically makes negligible contributions to the heat capacity. This is because these degrees of freedom are frozen because the spacing between the energy eigenvalues exceeds the energy corresponding to ambient temperatures (). In the following table such degrees of freedom are disregarded because of their low effect on total energy. Then only the translational and rotational degrees of freedom contribute, in equal amounts, to the heat capacity ratio.  This is why =}} for monatomic gases and =}} for diatomic gases at room temperature.

Contrary to the classical equipartition theorem, at room temperature, the vibrational motion of molecules typically makes negligible contributions to the heat capacity. This is because these degrees of freedom are frozen because the spacing between the energy eigenvalues exceeds the energy corresponding to ambient temperatures (). In the following table such degrees of freedom are disregarded because of their low effect on total energy. Then only the translational and rotational degrees of freedom contribute, in equal amounts, to the heat capacity ratio.  This is why =}} for monatomic gases and =}} for diatomic gases at room temperature.

与经典的'''<font color="#ff8000"> 能量均分定理</font>'''相反，在室温下，分子的振动对'''<font color="#ff8000"> 热容量</font>'''的贡献通常可忽略不计。这是因为这些自由度被冻结了，因为能量本征值之间的间隔超过了与环境温度（kBT）相对应的能量。在下表中，这些自由度均被忽略，因为它们对总能量的影响非常小。只有平移和旋转自由度对'''<font color="#ff8000"> 热容比</font>'''有些许贡献（等量）。这就是为什么在室温下，单原子气体{{mvar|γ}}={{math|{{sfrac|5|3}}}}和双原子气体{{mvar|γ}}={{math|{{sfrac|7|5}}}}的原因。

与经典的'''<font color="#ff8000"> 能量均分定理Equipartition theorem</font>'''相反，在室温下，分子的振动对'''<font color="#ff8000"> 热容量Heat capacity</font>'''的贡献通常可忽略不计。这是因为这些自由度被冻结了，因为能量本征值之间的间隔超过了与环境温度（kBT）相对应的能量。在下表中，这些自由度均被忽略，因为它们对总能量的影响非常小。只有平移和旋转自由度对'''<font color="#ff8000"> 热容比Heat capacity ratio</font>'''有些许贡献（等量）。这就是为什么在室温下，单原子气体{{mvar|γ}}={{math|{{sfrac|5|3}}}}和双原子气体{{mvar|γ}}={{math|{{sfrac|7|5}}}}的原因。