Development and Generalization of the Main Provisions of Equilibrium Thermodynamics Applied to General Quasi-Static Systems

A method for mathematical modeling of multidimensional quasi-static processes, which are generalization of quasi-static processes in equilibrium thermodynamics, is proposed and substantiated. A generalization of the first and second law of thermodynamics in the form of Carathéodory for multidimensional quasi-static processes is obtained. The idea of generalization is the construction of an orthogonal system of functionals similar to the functionals of work and heat of classical thermodynamics along families of phase trajectories corresponding to different types of actions on a multidimensional quasi-static system. The representation of quasi-static processes by systems of ordinary differential equations containing control variables is substantiated. The obtained results make it possible to apply a wide arsenal of methods from the theory of dynamic systems control to solve problems of quasi-static processes control.