更改

dN是在t时刻，关于（r，p）的微体积元<math> d^3\bf{r}</math>和微动量元<math> \mathrm{d}^3\bf{p}</math>内的分子数目。在位置空间和动量空间的一个区域上积分，得出在该区域中具有位置和动量的粒子总数：

dN是在t时刻，关于（r，p）的微体积元<math> d^3\bf{r}</math>和微动量元<math> \mathrm{d}^3\bf{p}</math>内的分子数目。在位置空间和动量空间的一个区域上积分，得出在该区域中具有位置和动量的粒子总数：

<math>N=\underset{momenta}\int\text{d}^{3}\mathbf{p}\underset{positions}\int\text{d}^{3}\mathbf{r}f(\mathbf{r},\mathbf{p},t)=\underset{momenta}\iiint\; \; \; \underset{positions}\iiint f(x,y,z,p_{x},p_{y},p_{z},t) \text{d}x\,\text{d}y\,\text{d}z\,\text{d}p_x\,\text{d}p_y\,\text{d}p_z</math>

<math>\begin{align}

N&=\underset{momenta}\int\text{d}^{3}\mathbf{p}\underset{positions}\int\text{d}^{3}\mathbf{r}f(\mathbf{r},\mathbf{p},t)

&=\underset{momenta}\iiint\; \; \; \underset{positions}\iiint f(x,y,z,p_{x},p_{y},p_{z},t)\; \text{d}x\,\text{d}y\,\text{d}z\,\text{d}p_x\,\text{d}p_y\,\text{d}p_z

\end{align}&lt;/math></math>

which is a [[multiple integral|6-fold integral]]. While ''f'' is associated with a number of particles, the phase space is for one-particle (not all of them, which is usually the case with [[deterministic]] [[many body problem|many-body]] systems), since only one '''r''' and '''p''' is in question. It is not part of the analysis to use '''r'''₁, '''p'''₁ for particle 1, '''r'''₂, '''p'''₂ for particle 2, etc. up to '''r'''_''N'', '''p'''_''N'' for particle ''N''.

which is a [[multiple integral|6-fold integral]]. While ''f'' is associated with a number of particles, the phase space is for one-particle (not all of them, which is usually the case with [[deterministic]] [[many body problem|many-body]] systems), since only one '''r''' and '''p''' is in question. It is not part of the analysis to use '''r'''₁, '''p'''₁ for particle 1, '''r'''₂, '''p'''₂ for particle 2, etc. up to '''r'''_''N'', '''p'''_''N'' for particle ''N''.