9) A classic modern standard text for the most general development of thermodynamics is Thermodynamics: An Introduction to the Physical Theories of Equilibrium Thermostatics and Irreversible Thermodynamics
by Herbert Callen (New York: John Wiley & Sons, 1960).
The assumption of a constitutive entropy flux is a straightforward generalization of the Gibbs-Duhem inequality, and one can prove that in simple cases it leads to the classical form and to the classical results both in irreversible thermodynamics
 and in thermoelasticity in particular .
Among his topics are the first and second laws of thermodynamics, entropy generation or exergy destruction, single-phase and multi-phase systems, chemically reactive systems, solar power, refrigeration, and irreversible thermodynamics
The domain of nonlinear dynamical systems and its mathematical underpinnings has been developing exponentially for a century, the last 35 years seeing an outpouring of new ideas and applications and a concomitant confluence with ideas of complex systems and their applications from irreversible thermodynamics
The conference and also this special issue feature contributions in different fields of continuum physics such as Extended Irreversible Thermodynamics
, Nonequilibrium Thermodynamics, Mesoscopic Continuum Physics, and Numerical Methods.
The authors assume readers are familiar with the concepts taught in introductory university courses in physics and chemistry, and cover basic laws of classical and irreversible thermodynamics
, phase equilibria, the thermodynamic theory of solutions, chemical reaction thermodynamics and kinetics, surface and interfacial phenomena, stressed systems, diffusion and statistical thermodynamics of gases and condensed matter.
The following major topics are discussed: basic laws of classical and irreversible thermodynamics
, phase equilibria, theory of solutions, chemical reaction thermodynamics and kinetics, surface phenomena, stressed systems, diffusion and statistical thermodynamics.
Among the several thermodynamic theories going beyond the local-equilibrium approach, Extended Irreversible Thermodynamics (EIT) provides generalized transport equations that incorporate memory and nonlocal effects, that reduce to the classical transport equations for low frequency and short mean-free paths, and that are able to incorporate the high-frequency behaviour of dissipative signals as, for instance, a finite speed of propagation of heat pulses, and general features of ballistic behaviour for long mean-free paths.
Extended Irreversible Thermodynamics was able to circumvent this problem by introducing a generalized entropy and entropy flux depending not only on the classical variables but also on the fluxes.
Extended Irreversible Thermodynamics provides a limited but fruitful framework to cope with these topics.
While linear irreversible thermodynamics
was fully developed in the middle 20th century, he says, a unified formulation of non-linear non-equilibrium thermodynamics is clearly needed, and he furthers that endeavor by reviewing classical and new elements of the phenomenological and the statistical approaches.