Because the phenomenological theories of phase transitions which are based on the equilibrium thermodynamics cannot describe the first-order phase transition processes accurately, the non-equilibrium thermodynamics was applied to extending the existing phenomenological theories of first-order phase transitions. First, the internal interactions of system at a first-order phase transition were considered. The nominal stress, the nominal volume force, the internal electric field and the internal magnetic field were introduced to characterize them. Then, the most general Gibbs equation except the factor of chemical reactions was established. Based on the conservation of energy and the transformation between internal energy and kinetic energy, the rate of local entropy production was deduced. Then based on the principle of minimum entropy production and the generalized Onsager reciprocal relations, the local, evolving characteristics of a first-order phase transition (e.g. a first-order ferroelectric phase transition) were described well. It makes up the inadequateness of the older phenomenological theories.