# Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics

## TL;DR

This paper explores how non-convex dissipation potentials influence stability and phase transitions in non-equilibrium thermodynamics, providing insights into complex fluid behaviors and supercritical boiling.

## Contribution

It introduces the concept of CR-stability related to dissipation potential convexity and develops evolution equations for perturbations in a thermodynamically consistent framework.

## Key findings

- Loss of convexity leads to dissipative phase transitions.
- CR-stability analysis explains complex fluid behaviors.
- Non-convex dissipation potentials relate to experimental phenomena.

## Abstract

Reformulating constitutive relation in terms of gradient dynamics (being derivative of a dissipation potential) brings additional information on stability, metastability and instability of the dynamics with respect to perturbations of the constitutive relation, called CR-stability. CR-instability is connected to the loss of convexity of the dissipation potential, which makes the Legendre-conjugate dissipation potential multivalued and causes dissipative phase transitions, that are not induced by non-convexity of free energy, but by non-convexity of the dissipation potential. CR-stability of the constitutive relation with respect to perturbations is then manifested by constructing evolution equations for the perturbations in a thermodynamically sound way. As a result, interesting experimental observations of behavior of complex fluids under shear flow and supercritical boiling curve can be explained.