Abstract

A recently developed approach to statistical thermodynamics shows that many paradigmatic mean-field models can be formulated in terms of c-integrable conservation laws of hydrodynamic type with prescribed initial conditions. Examples are the van der Waals model for isotropic fluids, the Curie-Weiss model for magnetism and generalised multi-partite spin systems. The occurrence of phase transitions in such models is explained naturally in terms of the breaking mechanism of nonlinear wave solutions to hyperbolic conservation laws, with the consequent emergence and propagation of classical (dissipative) shock waves. The talk aims at discussing this approach by analysing the discrete Maier-Saupe model for nematic liquid crystals with external fields and novel generalisations for so-called biaxial nematics via the study of a 4-component hydrodynamic-type system. The work presented is based on collaborations with Antonio Moro (Northumbria), Giulio Landolfi (Università del Salento) and Giovanni De Matteis (Università del Salento).