L. S. García‐Colín

On the foundations of extended irreversible thermodynamics

A theory of macroscopic systems which takes as independent variables the slow (conserved) ones plus the fast dissipative fluxes is carefully analyzed at three levels of description: macroscopic (thermodynamic), microscopic (projection operators) and mesoscopic (fluctuation theory). Such a description is compared with the memory function approach based only on the conserved variables. We find that the first theory is richer and wider than the second one, and some misunderstandings in this connection are clarified and discussed.

Fluids with internal degrees of freedom. I. Extended thermodynamics approach

Extended irreversible thermodynamics (EIT) is used to derive a complete set of time evolution equations for the state variables describing a general polyatomic fluid. The internal degrees of freedom of the fluid are represented by suitable nonconserved variables. In particular, these time evolution equations are shown to resemble relaxation‐type equations. The sign of the unknown coefficients included in such equations is undetermined. However, when a comparison is made with the results obtained from the moment solution method of a kinetic equation for a dilute polyatomic fluid, several of the general features of the phenomenological results are clarified. Indeed, the predictions of kinetic theory fully agree with the basic equations of EIT. This provides a mesoscopic foundation for the theory. The sign of the unknown coefficients appearing in the relaxation‐type equations for the nonconserved variables is such that the corresponding relaxation times are positive definite. Therefore, such equations are in...

A thermodynamic basis for transport phenomena in viscoelastic fluids

A calculation for the longitudinal stress modulus in a viscoelastic medium is obtained introducing the stress tensor, its trace and the heat flux as additional variables, without requiring the specific form of the dynamic structure factor of the system. By using extended irreversible thermodynamics, we derive the time evolution equations for the state variables. These equations are used to obtain general wave vector and frequency dependent expressions for measurable properties of the system. We recover for a particular case results that have been derived previously in the literature.

Extended thermodynamic description of diffusion in an inert binary mixture

The equilibrium concentration autocorrelation function for an inert binary mixture is calculated by means of extended irreversible thermodynamics. The ensuing generalized transport coefficient is explicitly evaluated and the corresponding k‐dependent relaxation time is also obtained. The connection with neutron scattering experiments is suggested and expressions for the dynamic structure factor and the half‐width dispersion relation are given.

Fluids with internal degrees of freedom. II. Rayleigh–Brillouin scattering

The extended thermodynamic treatment developed in part I for a fluid with internal degrees of freedom, is used to calculate its Rayleigh–Brillouin spectrum. A hydrodynamic model is first constructed which involves unspecified phenomenological coefficients. When these coefficients are identified in terms of experimental parameters, reasonably good agreement is obtained between the calculated and measured dynamic structure factor of CS2 at 20u2009°C with a density 1.262 g/cm3 and for k=8.608×10 cm−1. It is also shown that when the relaxation times of the trace and the nondeviatoric part of the stress tensor of the fluid tend to zero, the results previously derived by Mountain are recovered. The possible connections between this extended thermodynamic approach and Rytov’s hydrodynamic theory are also hinted at.

The underlying thermodynamic aspects of generalized hydrodynamics

Abstract We discuss the relation between extended irreversible thermodynamics and hydrodynamics. In particular, we derive systematically the results of the so-called generalized hydrodynamics and we relate our results with those of Mori and Zwanzigs theory, obtaining, thus, memory kernels compatible with irreversible thermodynamics.

On the Stokes-Einstein relation in glass forming liquids

Nowadays, the experimental evidence of a crossover between two dynamical regimes for supercooled glass-forming liquids at a temperature Tc,Tc>Tg, where Tg is the glass transition temperature, has been widely reported in the literature. On one hand, it is a well-known fact that in the region Tg<T<Tc, fragile glass forming liquids do not follow the Vogel–Fulcher–Tammann law. On the other hand, in the same region the Stokes–Einstein relation between the viscosity and the translational diffusion coefficient breaks down. Using the temperature derivative analysis, we present, for three glass-forming liquids, an empirical law for log10f, where f is the frequency, and we exhibit the break down of the Stokes–Einstein relation.

An H-theorem for the Enskog equation of a binary mixture of dissimilar hard spheres

Within the context of a standardlike Enskog theory, we prove the existence of both a global and a local H-theorem for a system consisting of a binary mixture of dissimilar hard spheres. The semipositive character of the entropy production, in addition to previous results on the proof of Onsager’s theorem, exhibits the complete compatibility of our theory with linear irreversible thermodynamics.

ULTRAFAST DIELECTRIC RELAXATION RESPONSE OF POLAR LIQUIDS

In this paper we calculate the complex dielectric constant of polar liquids for microwave and far-infrared range of frequencies. We use the formalism of extended irreversible thermodynamics (EIT) to obtain the autocorrelation function of the polarization vector. To this end, we introduce the local variation of the polarization flow as an independent variable, which allows for the description of collective interacting effects into the formalism. The results obtained here are compared with previous work in the so-called three-variable theory based on the Mori-Zwanzig projection operator technique. This comparison provides an interpretation of EIT in terms of a microscopic theory from which the role of the new independent variable can be established. Using the result of the complex dielectric constant presented here, we show that the fitting of experimental data in polar fluids can be improved in the far infrared frequencies.

COMPATIBILITY OF THE ENSKOG KINETIC-THEORY WITH HYDRODYNAMICS

It is proved in this paper that the condition that guarantees the compatibility of the Enskog kinetic theory with equilibrium thermodynamics guarantees also that the hydrodynamic transport coefficients calculated from the linearized Enskog kinetic theory possess the Onsager–Casimir symmetry.