Generalization of the thermodynamic approach to multi-dimensional quasistatic processes

Abstract

A method of mathematical modeling of multidimensional quasi-static processes, a generalization of quasi-static processes of equilibrium thermodynamics, is proposed and substantiated. The authors obtain a generalization of the first and the second law of thermodynamics in the form of Carathéodory to multidimensional quasi-static processes. The idea of generalization is to construct an orthogonal system of functionals similar to the work and heat functionals of classical thermodynamics along families of phase trajectories corresponding to different types of influences 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 use a wide arsenal of methods of the theory of control of dynamical systems to solve problems of control of quasi-static processes.