Quasi-Triviality and Universality of Integrable Conservation Laws and their Thermodynamic Interpretation

Antonio Moro, Northumbria University

Quasi-triviality is the property of systems of evolutionary PDEs that can be reduced to a system of hydrodynamic type via quasi-Miura transformations. The quasi-Miura transformation is a powerful tool to construct formal solutions to a PDE given a solution to the associated hydrodynamic type equation. 

We discuss the quasi-triviality of scalar conservation laws in relation with the classical method of transport equations  and the use of transport equations to effectively construct the quasi-Miura transformation.

Finally, we show how conservation laws of hydrodynamic type naturally arise in the study of general thermodynamic systems, how the quasi-Miura map can be used to deform classical equations of state, describe the state functions and their universal features.