Thermodynamic phase transitions and shock singularities

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 the 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 are also discussed.

revised version, 18 pages, 6 figures

Cited by in corpus (8)

• High-order QED correction impacts on phase transition of the Euler-Heisenberg AdS black hole
• Shock dynamics of phase diagrams
• Integrable extended van der Waals model
• Non-linear PDEs approach to statistical mechanics of Dense Associative Memories
• Complete integrability and equilibrium thermodynamics of biaxial nematic systems with discrete orientational degrees of freedom
• p-star models, mean field random networks and the heat hierarchy
• Integrable multi-phase thermodynamic systems and Tsallis' composition rule
• Symmetries and criticality of generalised van der Waals models