Thermodynamic phase transitions and shock singularities

de Nittis, Giuseppe and Moro, Antonio (2012) Thermodynamic phase transitions and shock singularities. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468 (2139). pp. 701-719. ISSN 1364-5021

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Official URL: http://dx.doi.org/10.1098/rspa.2011.0459

Abstract

We show that, under rather general assumptions on the form of the entropy function, the energy balance equation for a system in thermodynamic equilibrium is equivalent to a set of nonlinear equations of hydrodynamic type. This set of equations is integrable via the method of characteristics and it provides the equation of state for the gas. The shock wave catastrophe set identifies the phase transition. A family of explicitly solvable models of non-hydrodynamic type such as the classical plasma and the ideal Bose gas is also discussed.

Item Type: Article
Uncontrolled Keywords: shock singularities, phase transitions, equations of state, hydrodynamic systems
Subjects: F300 Physics
G100 Mathematics
Department: Faculties > Engineering and Environment > Mathematics and Information Sciences
Depositing User: Ay Okpokam
Date Deposited: 09 Apr 2013 08:33
Last Modified: 10 Aug 2015 11:14
URI: http://nrl.northumbria.ac.uk/id/eprint/12038

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