A physically based model is formulated for the active layer depth of permafrost under changing boundary condition instead of constant boundary condition considered in the traditional Stefan problem. Time varying ground heat flux is obtained from net radiation and surface temperature using the Maximum Entropy Production (MEP) model as the driver of the active layer melting process. Conductive heat flux at the melting front is approximated in terms of an analytical function of ground heat flux. The simulated active layer depth is in good agreement with the field observations.