Thermodynamics of fluids as a consequence of distribution theory for Diophantine equations
type: Item
instance of: scholarly article
title: Thermodynamics of fluids as a consequence of distribution theory for Diophantine equations
zbMATH Open document ID: 1179.80006
DOI: 10.1134/S0001434609070013
author: V. P. Maslov
published in: Mathematical Notes
publication date: 2009-10-27T00:00:00Z
review text: The author introduces the concept of ideal fluid considering 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. \(M\) is the global energy and \(N\) is the total number of particles. Taking \(\varepsilon _{i}=i^{\alpha }\) for some positive number \(\alpha \), the author claims that this leads to an abstract ideal thermodynamics. He then recalls the previous results he obtained concerning the transition via the condensate state in the parastatic, applying them to the scattering problem with Lennard-Jones potential. In a further refinement, he writes a similar problem than above in a two-phase state, separating the gas phase and the liquid phase with dimers and clusters, which leads to the notion of almost-ideal liquid. The last part of the paper contains an application of results concerning Diophantine equations to an abstract thermodynamics without the notion of pressure. The author computes the expression of the compressibility factor at temperatures below the Boyle temperature and finally claims that the values deduced from this expression are in good agreement with experimental graphs.
reviewed by: Alain Brillard
Mathematics Subject Classification ID: 80A05
Mathematics Subject Classification ID: 26A24
zbMATH DE Number: 5621797
zbMATH Keywords: dimer
zbMATH Keywords: cluster
zbMATH Keywords: parastatistic
zbMATH Keywords: condensate
zbMATH Keywords: dimension
zbMATH Keywords: gas
zbMATH Keywords: liquid
zbMATH Keywords: fluid
zbMATH Keywords: thermodynamics
zbMATH Keywords: distribution theory
zbMATH Keywords: Diophantine equation
MaRDI profile type: Publication
cites work: On the new distribution generalizing the Gibbs, Bose-Einstein, and Pareto distributions
cites work: Q4039838
cites work: New look at thermodynamics of gas and at clusterization
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description: scientific article; zbMATH DE number 5621797