Model of extreme intermediate states MEIS

Currently the authors are developing three classes of models of extreme intermediate states (MEIS) (1) with variable parameters (2) with variable flows, and (3) those describing spatially inhomogeneous systems. All these classes of the models are formulated and analyzed in terms of MP, which, in the authors opinion, can be defined as a mathematical theory of equilibrium states. It is natural to start the analysis of the created modifications with the MEIS with variable parameters, which is the closest in character to the traditional equilibrium thermodynamics models. 

The main idea of the research being described is the refusal to use an equation of trajectory and construction of stepwise methods to analyse processes on the basis of the model of extreme intermediate states (MEIS) that was created by B.M.Kaganovich, S.P.Filippov and E.G. Antsiferov (Antsiferov et al., 1988 Kaganovich, 1991 Kaganovich et al., 1989). The features that make MEIS different from the traditional thermodynamic models are 1) statement of the problem to be solved (instead of search for a sole point of final equilibrium the entire set of thermodynamic attainability Dj(y) from the given initial state y is considered and the states with extreme values of modeled system characteristics of interest to a researcher are found) 2) dual interpretation of the equilibrium notion, i.e. both as a state of rest and as an instant of motion in which the equality of action and counteraction is observed and 3) dual interpretation of dynamic quantities (work t, heat q, rate w, flow of substance x, etc.) both... 

Though in formulations of MEIS of type (7)-(12) or the particular form (53)-(57) the possibility of projecting the space of thermodynamic variables to a tree is not shown, the knowledge of principal possibility to reduce the set Dt(y) to the tree makes the analysis of capabilities and comparative merits of the model of extreme intermediate states essentially easier, clearer, and more convincing. 

Relations between the theories of states and trajectories and capabilities of equilibrium thermodynamic analysis to study reversible and irreversible kinetics can be more fully revealed by considering another type of models of extreme intermediate states, namely MEIS of hydraulic circuits (Gorban et al., 2001, 2006 Kaganovich et al., 1997, 2007, 2010). Convenience and clearness of using these models to describe the considered problems are determined by the fact that they are intended to study an essentially irreversible process, i.e. motion of a viscous fluid. Besides, they can be treated as models of the mechanism of fluid transportation from the specified source nodes of a hydraulic system to the specified consumption nodes. The major variable of the hydraulic circuit theory (Khasilev, 1957,1964 Merenkov and Khasilev, 1985), i.e. continuous medium flow, has an obvious kinetic sense. 

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See also in sourсe #XX -- [ ]

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