only of the deformation at given instant, but also on the local lattice
velocity. The integration over the Brillouin zone does not commutate with the
differentiation with respect to the time and the coordinates.
As a result some fluxes appear
through the zone boundaries. This effect is important for nonequilibrium
systems, open Fermi-surfaces as well as for other cases
when the partition function or
its derivatives do not vanish on the zone boundaries.
This inconvenience can be
passed over by introducing a renormalized partition function
\begin{equation}
\varphi(\mbox {\boldmath $\kappa$}, {\bf r},t) = f/\sqrt{g} .$$

The kinetic equation for $\varphi(\mbox{\boldmath $\kappa$},
 {\bf
r},t)$ has the form $$\begin{aligned}
\dot{\varphi}  &  +  &  \div \left\{\left(\dot{\bf u} + {\bf
a}_{\alpha}
\frac{\partial\eps}{\partial \kappa_{\alpha}}\right)\varphi\right\}
-{\bf  a}_{\alpha} \frac{\partial}{\partial \kappa_{\alpha}} \left\{\varphi
\left(\nabla\eps + m \frac{\d \dot{\bf
u}}{\d t}\right )\right. \nonumber \\
& - &\left. m\varphi \frac{\partial\eps}{\partial  \kappa_{\beta}}
{\bf a}_{\beta}\times \curl\dot{\bf u} -  {\bf
F}\varphi\right\}  = \hat{I}\varphi .\end{aligned}$$ In this notation the differentiation with respect to $t$ and [**r**]{} is carried out at constant [$\kappa$]{} and hence commutates with $\int d^3
\kappa$. Results obtained by such a procedure can easily be rewritten in the previously adopted variables by the following substitutions $${\bf a}_\alpha \frac{\partial}{\partial \kappa_\alpha}
\leftrightarrow
\frac{\partial}{\partial{\bf k}} \leftrightarrow
