The Boltzmann Transport Equation

Abstract

The non-relativistic Boltzmann equation is given by

$$\displaystyle\begin{array}{rcl} \frac{\partial f} {\partial t} +\boldsymbol{ v} \cdot \nabla _{\boldsymbol{r}}f + \frac{\boldsymbol{F}} {m} \cdot \nabla _{\boldsymbol{v}}f = \left (\frac{\delta f} {\delta t} \right )_{coll},& &{}\end{array}$$

(2.1)

where $\boldsymbol{r},\boldsymbol{v}$, and t are independent variables.