Thermodynamic phase transitions and shock singularities

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.

💡 Research Summary

The paper develops a unified mathematical framework that connects thermodynamic phase transitions with shock‑wave singularities by recasting the energy balance of a system in equilibrium into a set of nonlinear hyperbolic conservation laws. Starting from the differential form of the first law,
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