  Evolution of charged quantum fields under the action of constant nonuniform
electric fields is studied. To this end we construct a special generating
functional for density operators of the quantum fields with different initial
conditions. Then we study some reductions of the density operators. For
example, reductions to electron or positron subsystems, reduction induced by
measurements, and spatial reduction to the left or to the right subsystems of
final particles. We calculate von Neumann entropy for the corresponding reduced
density operators, estimating in such a way an information loss. Then we
illustrate the obtained results by calculations in a specific background of a
strong constant electric field between two infinite capacitor plates separated
by a finite distance $L$.
