Application of the thermodynamic extremal principle to modeling of thermodynamic processes in material sciences

An extremal principle is formulated for thermodynamic systems near equilibrium subjected to various external conditions. It is shown that the principle describes unambiguously the kinetics of the thermodynamic system and replaces classical phenomenological equations. The global formulation of the principle makes it possible i) to introduce discrete characteristic parameters for the proper description of the state and evolution of the system, ii) to take into account constraints amongst the characteristic parameters of the local or global character and iii) to derive the evolution equations for the characteristic parameters. These facts turn the principle into an effective tool for the treatment of non-equilibrium thermodynamic systems.