Thermodynamic Modeling on Graphs

The question on the effectiveness of geometrical methods for development and interpretation of extreme thermodynamic models is evidently subject to essential subjectivism and partiality. So, whereas Newton in his Principles started to solve each of more than 200 considered problems with graphical explanations, and only then passed to formulas, Lagrange in Mechanique Analytique did not present any drawings, demonstrating thus the possibility of constructing the “building” of mechanics without graphical representation. Though in thermodynamics, geometrical methods have been applied starting with Gibbs’s classical works, in the works known to the authors on computer modeling of thermodynamic systems, such methods have not been practically used. Our reference to graphical construction is based on the assumption that graphs should provide an insight into mathematical peculiarities of the problems solved, on the one hand, and contribute to expansion of the sphere for applications of extreme models, on the other. Yet Kirchhoff had shown the possibility of reducing problems dealing with the study on multidimensional systems to problems on graphs. In [111] he tested the revealed theoretical relationships for current and potential distribution in the flat round plate by comparison with the experimental results on the electric circuit, i.e., on the object with the scheme in a graph form. Thus, he established the correspondence between electric fields in the continuous two-dimensional space and on the one-dimensional continuum, i.e., the “graph.” Kirchhoff deduced his known laws of current distribution for graphs and showed in [112] how to derive an independent system of equations by using these laws, choosing the calculated