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

Microscopic cut-off dependence of an entropic force in interface propagation of stochastic order parameter dynamics