Forces due to fluctuations in the anisotropic phase-field model of solidification

Stochastic forces due to thermodynamic fluctuations are derived for the anisotropic phase-field model of solidification. The stochastic forces turn out to be anisotropic. The derivation utilizes the general principles of irreversible thermodynamics. One of the forces is the divergence of the stochastic heat flux derived by Landau and Lifshitz (Statistical Physics, Pergamon Press, Oxford, 1958). The other force is the phase-field counterpart of the interface force introduced by Karma (Phys. Rev. E 48 (1993) 3441).