  The Vlasov equation embodies the smooth field approximation of the
self-consistent equation of motion for charged particle beams. This framework
is fundamentally altered if we include the fluctuating forces that originate
from the actual charge granularity. We thereby perform the transition from a
reversible description to a statistical mechanics' description covering also
the irreversible aspects of beam dynamics. Taking into account contributions
from fluctuating forces is mandatory if we want to describe effects like
intrabeam scattering or temperature balancing within beams. Furthermore, the
appearance of ``discreteness errors'' in computer simulations of beams can be
modeled as ``exact'' beam dynamics that is being modified by fluctuating
``error forces''. It will be shown that the related emittance increase depends
on two distinct quantities: the magnitude of the fluctuating forces embodied in
a friction coefficient $\gamma$, and the correlation time dependent average
temperature anisotropy. These analytical results are verified by various
computer simulations.
