  Statistical plasma theory far from thermal equilibrium is subject to
Liouville's equation which is at the base of the BBGKY hierarchical approach to
plasma kinetic theory from which in the absence of collisions Vlasov's equation
follows. It is also at the base of Klimontovich's approach which includes
single particle effects like spontaneous emission. All these theories have been
applied to plasmas with admirable success even though they suffer from a
fundamental omission in their use of the electrodynamic equations in the
description of the highly dynamic interactions in many-particle particle
conglomerations. In the following we extend this theory to taking into account
that the interaction between particles separated from each other at a distance
requires the transport of information. Action needs to be transported and thus
in the spirit of the direct-interaction theory as developed by Wheeler and
Feynman (1945) requires time. This is done by reference to the retarded
potentials. We derive the fundamental Liouville equation for the phase space
density of a system composed of a very large number of charged particles.
Applying the approach of Klimontovich (1967) we obtain the retarded time
evolution equation of the one-particle distribution function in plasmas which
replaces Klimontovich's equation in cases when the direct-interaction effects
have to be taken into account. This becomes important in all systems where the
distance between two points $|\Delta \vec{q} | \sim ct$ is comparable to the
product of observation time and light velocity, which is typical in cosmic
physics and astrophysics.
