An alternative approach, non-equilibrium evolution thermodynamics, was compared with the classical Landau approach. A statistical justification of the approach was offered with the help of a probability distribution function for the example of a solid with vacancies. Two kinds of kinetic equation were derived in terms of the internal energy and the modified free energy. For fast processes, thermal fluctuations had no time to exert any essential influence and it thus became possible to treat the problem in the mean-field approximation. The approach was based not upon an abstract order parameter but upon the physical parameters of structural defects; their quantity (density) and average energy. An alternative, more general, form of the kinetic equations, symmetrical with respect to the internal energy and the modified configurational free energy, was proposed. In this case, the density of defects and defect energy were interrelated by symmetrical differential dependences. As in the stationary state, the defect energy was not zero. In the framework of non-equilibrium evolution thermodynamics, the extremum principle of equality-to-zero of the derivative of the (modified) free energy with respect to the so-called order-parameter broke down. This principle had to be replaced by the principle of tendency to a stationary state. Stationary-state characteristics could not be determined within the framework of the phenomenological approach, so statistical and microscopic approaches were required. The present form of the kinetic equations was generalized to all types of regular and randomly distributed defects.

Nonequilibrium Evolution Thermodynamics of Vacancies. L.S.Metlov: Physical Review Letters, 2011, 106[16], 165506