  Relaxation of the thermal Casimir or van der Waals force for a model
dielectric medium is investigated. We start with a model of interacting
polarization fields with a dynamics that leads to a frequency dependent
dielectric constant of the Debye form. In the static limit the usual zero
frequency Matsubara mode component of the Casimir force is recovered. We then
consider the out of equilibrium relaxation of the van der Waals force to its
equilibrium value when two initially uncorrelated dielectric bodies are brought
into sudden proximity. It is found that the spatial dependence of the out of
equilibrium force is the same as the equilibrium one but it has a time
dependent amplitude, or Hamaker coefficient, which increases in time to its
equilibrium value. The final relaxation to the equilibrium value is exponential
in systems with a single or finite number of polarization field relaxation
times. However, in systems, such as those described by the Havriliak-Negami
dielectric constant, with a broad distribution of relaxation times, we observe
a much slower power law decay to the equilibrium value.
