  The steady propagation of a $(d-1)$-dimensional planer interface in
$d$-dimensional space is studied by analyzing mesoscopic non-conserved order
parameter dynamics with two local minima under the influence of thermal noise.
In this analysis, an entropic force generating interface propagation is
formulated using a perturbation method. It is found that the entropic force
singularly depends on an ultraviolet cut-off when $d \ge 2$. The theoretical
calculation is confirmed by numerical simulations with $d=2$. The result means
that an experimental measurement of the entropic force provides an estimation
of the microscopic cut-off of the mesoscopic description.
