New approach to classical thermodynamics

Mathematical notes. 2016. Vol. 100. No. 1. P. 154–185.

The author constructs a new conception of thermodynamics which is based on new results in number theory. We consider a maximally wide range of gases, liquids, and fluids to which, in principle, the Carathéodory approach can be applied. The Carathéodory principle is studied using the Lennard-Jones potential as an example. On the basis of this example, we analyze the dispersive structure of a fluidwhose density exceeds the critical value. We introduce a new parameter, the “jamming factor,” which determines the jamming effect for such fluids. A comparison with experimental data for nonpolar molecules is carried out. The phase transition “liquid-amorphous solid” is studied in detail in the domain of negative pressures. We discuss the theoretical relationship between the obtained solutions and econophysics, some mysteries in biology, and other sciences.

Ключевые слова: Zeno line, Bose–Einstein distribution, Lagrangian manifold, Bachinskii condition, Lennard-Jones potential, Gentile correction, Carathéodory conception, contact manifold, dispersive medium, entropy production, Fermi–Dirac distribution, Hougen–Watson diagram, Legendre manifold, phase transition “liquid-amorphous solid”, van der Waals equation of state, van der Waals law of corresponding states