  Field dynamics in a rapidly expanding system is investigated by transforming
from space-time to the rapidity - proper-time frame. The proper-time dependence
of different contributions to the total energy is established. For systems
characterized by a finite momentum cut-off, a freeze-out time can be defined
after which the field propagation in rapidity space ends and the system decays
into decoupled solitons, antisolitons and local vacuum fluctuations. Numerical
simulations of field evolutions on a lattice for the (1+1)-dimensional $\Phi^4$
model illustrate the general results and show that the freeze-out time and
average multiplicities of kinks (plus antikinks) produced in this 'phase
transition' can be obtained from simple averages over the initial ensemble of
field configurations. An extension to explicitly include additional dissipation
is discussed. The validity of an adiabatic approximation for the case of an
overdamped system is investigated. The (3+1)-dimensional generalization may
serve as model for baryon-antibaryon production after heavy-ion collisions.
