Metlov, Leonid S. “Nonequilibrium evolution thermodynamics of vacancies.” Physical review letters 106, no. 16 (2011): 165506.
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An alternative approach, nonequilibrium evolution thermodynamics, is compared with the classical Landau approach. A statistical justification of the approach is done with the help of a probability distribution function on an example of a solid with vacancies. Two kinds of kinetic equations are derived in terms of the internal energy and the modified free energy.