Symmetries and criticality of generalised van der Waals models

TL;DR

This paper investigates the symmetry properties and critical behavior of a broad class of generalized van der Waals models, focusing on their thermodynamic solutions and phase coexistence dynamics.

Contribution

It introduces a framework to analyze the symmetry and criticality of generalized van der Waals models using asymptotic expansions and thermodynamic relations.

Findings

Identifies symmetry conditions for thermodynamic solutions.

Derives critical properties from coexistence curve dynamics.

Provides insights into phase transition behavior in generalized models.

Abstract

We consider a family of thermodynamic models such that the energy density can be expressed as an asymptotic expansion in the scale formal parameter and whose terms are suitable functions of the volume density. We examine the possibility to construct solutions for the Maxwell thermodynamic relations relying on their symmetry properties and deduce the critical properties implied in terms of the the dynamics of coexistence curves in the space of thermodynamic variables.