A Review of modern non-equilibrium thermodynamics theories

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Looking for thorough serious comparative review of modern generalisations of classical non-equilibrium thermodynamics of continua.

I have heard about several such generalisations:
1) rational mechanics by Truesdell, Coleman, Noll.
2) extended thermodynamics by Müller (and Ruggeri).
3) the GENERIC formalism by Gřmela and Öttinger.

Probably, there are more (Gyarmati or Meixner approaches, for example). Almost every single one of the persons, whose names are listed above, has published a monograph or at least a vast collection of research papers devoted to the subject. But all my efforts to find an objective comparative (at least relatively modern!) review of the existing theories were futile.

I would be grateful for a reference. Just to make myself clear, I am not interested in papers/monograph describing single approach and barely mentioning the others only to proceed to impressive array of applications of the selected theory ranging from galaxy cluster formation to hydrodynamics of viscous flow in porous media to ant colonies dynamics. I am looking for thoughtful and deep unbiased analysis of corner stones and comparison of features of the theories in stead (it is perfectly fine if it involves some serious math).
 

Andy Resnick

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Looking for thorough serious comparative review of modern generalisations of classical non-equilibrium thermodynamics of continua.

I'd be interested in suitable sources as well. All I have now is a short intro chapter in
D. Jou, ‎J. Casas-Vazquez, ‎ and G. Lebon's book "Extended Irreversible Thermodynamics"
 

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All I have now is a short intro chapter in D. Jou, ‎J. Casas-Vazquez, ‎ and G. Lebon's book "Extended Irreversible Thermodynamics"
Thank you, I checked the monograph you cited. For now it looks like the best shot. But actually, I was thinking about something deeper and more thorough (probably a journal review paper).

Some critique of basics and upshots of rational thermodynamics approach can be found in «A history of thermodynamics» by Ingo Müller. But I have my doubts it could be considered as unbiased (Müller is the father of an alternative approach).
 

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