Gyula Tóth^{1}, Tamás Pusztai^{2}, Bjørn Kvamme^{3}, László Gránásy^{2,4}

^{1}Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, U.K.

^{2}Institute for Solid State Physics and Optics, Wigner Research Centre for Physics, P.O. Box 49, Budapest H-1525, Hungary

^{3}Institute of Physics and Technology, University of Bergen, Allégaten 55, N-5007 Bergen, Norway

^{4}BCAST, Brunel University, Uxbridge, Middlesex, UB8 3PH, United Kingdom

A multiphase-field theory is presented that describes interface driven multi-domain dynamics. The free energy functional and the dynamic equations are constructed on the basis of criteria of mathematical and physical consistency. First, it is demonstrated that the most widely used multiphase theories are physically inconsistent, therefore, a new theory has to be developed. Combining elements of the investigated models with a new multivariate generalization of the free energy surface results in a general multiphase / multi-component theory, which keeps the variational formalism, reduces / extends naturally on the level of both the free energy functional and the dynamic equations, utilizes arbitrary pairwise equilibrium interfacial properties, features equilibrium = stationary equivalency, and avoids the appearance of spurious phases.