  Nonequilibrium behaviors of positional order are discussed based on diffusion
processes in particle systems. With the cumulant expansion method up to the
second order, we obtain a relation between the positional order parameter
$\Psi$ and the mean square displacement $M$ to be $\Psi \sim \exp(- {\bf K}^2 M
/2d)$ with a reciprocal vector ${\bf K}$ and the dimension of the system $d$.
On the basis of the relation, the behavior of positional order is predicted to
be $\Psi \sim \exp(-{\bf K}^2Dt)$ when the system involves normal diffusion
with a diffusion constant $D$. We also find that a diffusion process with
swapping positions of particles contributes to higher orders of the cumulants.
The swapping diffusion allows particle to diffuse without destroying the
positional order while the normal diffusion destroys it.
