Continuum Mechanics and Thermodynamics

, Volume 30, Issue 4, pp 917–941 | Cite as

Non-convex dissipation potentials in multiscale non-equilibrium thermodynamics

  • Adam Janečka
  • Michal Pavelka
Original Article


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 (CR-extension). As a result, interesting experimental observations of behavior of complex fluids under shear flow and supercritical boiling curve can be explained.


Gradient dynamics Non-Newtonian fluids Non-convex dissipation potential Legendre transformation Stability Non-equilibrium thermodynamics 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematical Institute, Faculty of Mathematics and PhysicsCharles University in PraguePragueCzech Republic

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