粗視化

${\displaystyle F={\frac {1}{A_{\delta \Gamma }}}\int _{\delta \Gamma }fd\Gamma }$

${\displaystyle F(p,x)={\frac {1}{\Delta p\Delta x}}\int _{p_{j}}^{p_{j}+\Delta p}\int _{x_{i}}^{x_{i}+\Delta x}f({\bar {p}},{\bar {x}})d{\bar {p}}d{\bar {x}}}$　但し　${\displaystyle p_{j}\leq p<p_{j+1},\ x_{i}\leq x<x_{i+1}}$

${\displaystyle S[F]=-k_{B}\int F\ln F\ dpdx}$

${\displaystyle S[f]=-k_{B}\int f\ln f\ dpdx}$

${\displaystyle {\frac {dS[f]}{dt}}=-k_{B}\int \left(1+\ln f\right){\frac {df}{dt}}\ dpdx}$

${\displaystyle {\frac {df}{dt}}={\frac {\partial f}{\partial t}}+{\frac {\partial f}{\partial p}}{\dot {p}}+{\frac {\partial f}{\partial x}}{\dot {x}}=0}$

${\displaystyle {\frac {dS[f]}{dt}}=0}$

${\displaystyle w={\frac {N!}{\prod _{i}n_{i}!}}}$

${\displaystyle \left.s=k_{B}\ln w\right.}$

${\displaystyle W={\frac {N!}{\prod _{cg}n_{cg}!}}}$

${\displaystyle \left.S=k_{B}\ln W\right.}$