  In a homogeneous pionic gas system, chemical nonequilibrium process is
considered to understand its effect in the expansion processes that are
realized immediately after heavy ion collisions. The chemical relaxation time
is calculated by incorporating the $\pi+\pi \leftrightarrow \pi+\pi+\pi+\pi$
reaction, which is given in the second order of perturbation in the $\sigma$
model. The $\pi+\pi \leftrightarrow \pi+\pi+\pi+\pi$ reaction is assumed to be
less frequent than the $\pi+\pi \leftrightarrow \pi+\pi$ scattering that is
expected to establish the local equilibrium, and hydrodynamical equation is
solved for various initial conditions. It is shown that the relaxation time is
of the order of 100fm and does not have a significant effect on the expansion
process, which implies that the pion number freezeout takes place at an early
stage of the expansion.
