Non-equilibrium linear thermodynamics represents an effective tool for phenomen-ological description of processes in solids. It introduces local internal state variables as the mole fractions of individual components and provides evolution equations for them in the form of partial differential equations. Materials science has to treat rather complex systems and characterizes them by means of a limited number only of characteristic parameters (CPs) and their evolution, which can be extracted from the solution ofpartial differential equations. If, however, one utilizes Thermodynamic Extremal Principle (TEP) formulated in CPs, the task becomes much easier. Thus, the TEP can be considered a convenient tool for modelling which has been applied successfully to sintering, creep and rafting in superalloys, grain growth and precipitate coarsening or kinetics of precipitation, for example (in the program MatCalc).

In this chapter the TEP is presented in its general form as well as in discrete CPs. Its general form is used for the derivation of diffusion and creep equations in mechanically loaded multi-component systems with non-ideal sources and sinks for vacancies. The TEP formulated in discrete CPs is used for derivation of equations for grain growth and coarsening within the multi-object concept and distribution concept. Both concepts are compared successfully in an example for grain growth with initial bi-modal size distribution. The TEP is used in modelling of precipitation in solid multi-phase, multi-component systems. Comparison of an example with experiment indicates good applicability of the model in the prediction of and description of the evolution in rather complex systems.