A proper description of the dissipation in a forcing-dissipative system, such as the atmosphere, is very important when the system is discretized. Atmospheric dissipation is generally treated as diffusion in numerical weather prediction (NWP) models. The commonly used fourth-order diffusion scheme (linear and nonlinear) generates spurious upgradient mass or heat transport, which violates the entropy constraint posed by non-equilibrium thermodynamics. The second law of thermodynamics is used in this paper to re-construct the diffusion scheme to ensure downgradient transport. The new physics-based scheme is applied to the Penn State/NCAR non-hydrostatic mesoscale model. A hurricane case simulation demonstrates that the new scheme improves the model accuracy in predicting the strength of the hurricane.