2.2.2.1 Non-Equilibrium State

If a closed system is in a state in which some of its parts have physical quantities different from their statistical averages, the system is in a non-equilibrium state. It is assumed that a non-equilibrium state can be described by a non-equilibrium distribution function $f_{n}(\vec{r},\vec{k},t)$ which now depends on time. The electron number in band $n$ at time $t$ in the phase space volume $d\vec{r}d\vec{k}$ around point $(\vec{r},\vec{k})$ is equal to:

$$dN_{el}=f_{n}(\vec{r},\vec{k},t)\frac{d\vec{r}d\vec{k}}{4\pi^{3}}.$$ (2.36)

When a closed system approaches its equilibrium the non-equilibrium distribution function tends to the equilibrium distribution (2.30). S. Smirnov: