Abstract
The main purpose of this review is to summarize the recent advances of the Conservation–Dissipation Formalism (CDF), a new way for constructing both thermodynamically compatible and mathematically stable and well-posed models for irreversible processes. The contents include but are not restricted to the CDF’s physical motivations, mathematical foundations, formulations of several classical models in mathematical physics from master equations and Fokker–Planck equations to Boltzmann equations and quasi-linear Maxwell equations, as well as novel applications in the fields of non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave propagation/transportation in geophysics and neural science, soft matter physics, etc. Connections with other popular theories in the field of non-equilibrium thermodynamics are examined too.
Highlights
IntroductionThe last half century has witnessed a rapid progression in non-equilibrium thermodynamics, which has become an exciting and fruitful research field in modern physics
The last half century has witnessed a rapid progression in non-equilibrium thermodynamics, which has become an exciting and fruitful research field in modern physics.Non-equilibrium thermodynamics abandons several ideal assumptions of the equilibrium approach and leads to much broader and realistic studies beyond equilibrium
This part goes through several novel applications of Conservation– Dissipation Formalism (CDF) relating to non-Fourier heat conduction, non-Newtonian viscoelastic fluids, wave transportation in neuroscience, soft matter physics and boundary control problem with an effort to sketch the backgrounds of these diverse fields and to present basic results derived from CDF
Summary
The last half century has witnessed a rapid progression in non-equilibrium thermodynamics, which has become an exciting and fruitful research field in modern physics. Grmela [8] proposed a Hamiltonian version of nonequilibrium thermodynamic theory, which is subsequently developed into the general equation for the non-equilibrium reversible-irreversible coupling (GENERIC) form by Grmela and Öttinger [9,10]. Established on the modern theory of first-order hyperbolic equations, conservationdissipation formalism of irreversible thermodynamics (CDF) can be seen as a mathematically regularized theory of EIT and GENERIC. We apply CDF to derive unknown constitutive relations in various fields, including viscoelastic fluids, heat conduction, soft matter physics, geophysics, and so on.
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