ASSIGNMENT OF STATE FUNCTIONS FOR INTERACTION POTENTIALS, REDUCED HEAT CAPACITIES AND REDUCED THERMAL
EFFECTS INCLUDED IN THE EQUATIONS OF THE METHOD OF MATHEMATICAL PROTOTYPING OF ENERGY PROCESSES 

Igor E. Starostin, Doctor of technical sciences, professor, professor of the sub-department of electrical engineering and aviation electrical equipment, Moscow State Technical University of Civil Aviation (20 Kronshtadtskiy boulevard, Moscow, Russia), E-mail: starostinigo@yandex.ru
Stanislav I. Gavrilenkov, Head of the educational laboratory of the sub-department of electrical engineering and aviation electrical equipment, Moscow State Technical University of Civil Aviation (20 Kronshtadtskiy boulevard, Moscow, Russia), E-mail: gavrilenkov@mstuca.ru

Background. The main requirements for mathematical models applicable to solving practical problems of modern engineering and technology are their accuracy and adequacy (i.e., non-contradiction with physical and chemical laws). To construct such models of systems of various physical and chemical nature, a method of mathematical prototyping of energy processes was proposed within the framework of mechanics, electrodynamics and modern nonequilibrium thermodynamics, which yields models that do not contradict general physical laws (the laws of thermodynamics, mechanics and electrodynamics) and the physical features of the system under consideration. To implement the equations of the above-mentioned method in numerical form, it is necessary to correctly specify, with an accuracy of experimentally studied constant coefficients, the state function for the properties of substances and processes. In particular, the state functions for interaction potentials, reduced inverse heat capacities and reduced thermal effects – the condition of the total differential of entropy and internal energies. The present work is devoted to specifying the above-mentioned state functions that satisfy the above-mentioned conditions. Matherials and methods. The synthesis of equations of the dynamics of physical and chemical processes is carried out on the basis of the method of mathematical prototyping of energy processes. The assignment of state functions for interaction potentials, reduced inverse heat capacities and reduced thermal effects is carried out by assigning independent components of the mentioned functions with subsequent integration of the necessary and sufficient conditions of the total differential of entropy and internal energies. The mentioned independent components are constructed by methods of identification theory, in particular by methods of symbolic regression. Results. The proposed method for specifying state functions for interaction potentials, reduced reciprocal heat capacities and reduced thermal effects gives correct state functions for the mentioned quantities. Conclusions. The proposed method for constructing state functions that satisfy the above-mentioned conditions of the total differential reduces the construction of a system model based on the method of mathematical prototyping of energy processes to the use of classical identification methods (in particular, symbolic regression methods).

method of mathematical prototyping of energy processes, state functions, conditions of total differential, correctness of models

Starostin I.E., Gavrilenkov S.I. Assignment of state functions for interaction potentials, reduced heat capacities and reduced thermal effects included in the equations of the method of mathematical prototyping of energy processes. Nadezhnost' i kachestvo slozhnykh sistem = Reliability and quality of complex systems. 2025;(1):36–43. (In Russ.). doi: 10.21685/2307-4205-2025-1-5