Variational properties of irreversible processes

Gyarmati’s Variational Principle of Dissipative Processes

“…From this principle, the parabolic transport equations of irreversible transport processes can be derived both in the linear and quasi-linear case, as well as in all those non-linear cases where dissipation potentials can be determined by Equations (23) and (24), due to the validity of the generalized reciprocal relations in Equation (11) [20,21,35,37,39,41,42,[56][57][58][59]84]. The application of the governing principle can be understood through the properties of the local principle.…”

“…Both representations were widely applied to the solution of several practical problems [41][42][43]56,57,85]. It is also well known that the force representation of Gyarmati's governing principle is equivalent to the local potential method of Prigogine and Glansdorff [86], while the flux representation is the equivalent of the variational methods of Biot [18,19].…”

“…This principle was applied to several fields of irreversible processes: first of all, by his colleagues (Verhás [33], Böröcz [34], Farkas [35,36], Sándor [37], Vincze [38][39][40] and Stark [41,42]); but also by many others (Singh [43,44], Bhattacharya [45,46], Dickel [47,48], etc. ).…”

Mathematical and Physical Foundations of Drying Theories

“…However, in many practical applications it is imponant to model systems, which can be described with quasi-linear or even nonlinear PDEs. For such cases the so-called force representation of the general variational principles of the irreversible thermodynamics (Glansdorff and Prigogine, 1971) gives the following relationship (Stark, 1975):…”

“…that at boundaries of their domains C2 ( x 4 ) they satisfy the same (type of) boundary conditions. For the sake of simplicity only one dimensional problems are discussed here, whose direct generalisation to multidimensional cases is relatively simple (Gelfand and Fomin, 1963) and will say, that the functions from (Gelfand and Fomin, 1963;Stark, 1975;Zienkiewicz 1977;Lebedev, 1997) from which the best-known direct methods in the calculus of variation are: the Ritz and the Ritz-Galerkin method. It must also be mentioned, that the variational methods have reached a remarkable degree of generality, i.e.…”