Thermodynamics of fluids for a relativistic gas as a consequence of distribution theory for Diophantine equations
The main part of the paper consists to describe some properties of a function \(H\) which plays the role of an Hamiltonian, assuming that it is smooth and that \(H(p)\) goes to 0 when \(p\) goes to 0 not faster than an arbitrarily large power of \(p\). This is applied to the study of the system \( \sum_{i=1}^{s}\varepsilon _{i}N_{i}\leq M\); \(\sum_{i=1}^{s}N_{i}=N\), where \(M \), \(\varepsilon _{i}\) and \(N\) are given numbers, \(N_{i}\) is a positive integer and \(N\) is an integer. This system is linked to thermodynamics. Taking an example of Hamiltonian \(H\), the author deduces some properties of the particles of a relativistic gas. Then the author moves to a two-phase state and the paper ends with the computation of the compressibility factor of an abstract ideal two-phase thermodynamics.
scientific article; zbMATH DE number 5621828