Weakly nonlocal irreversible thermodynamics

Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer‐Krumhansl, Ginzburg‐Landau and Cahn‐Hilliard type equations.     

Time-scaling in irreversible thermodynamics

We consider linear dynamical systems with motions characterized by two different time-scales. In practice the dynamical matrix in the phenomenological equations of motion often exhibits a strong coupling of the slow and fast variables. It is shown on the basis of the Onsager symmetry relations that a simple transformation of variables leads to a weak coupling. After the transformation one can use perturbation theory to derive reduced matrices describing the slow (fast) motions of the slow (fast) subsystem.     

On the relationship between fluctuating irreversible thermodynamics and “extended” irreversible thermodynamics

The relationship between fluctuating irreversible thermodynamics and theories of irreversible processes which include the thermodynamic fluxes as independent variables is explored. It is shown that the usual fluctuating linear theory of irreversible thermodynamics is a contraction of the extended theory. This contraction contains non-Markovian effects dependent upon the relaxation times associated with the thermodynamic fluxes. In the limit that these relaxation times are small, the extended theory is shown to be equivalent to the usual fluctuating thermodynamic theory. A critique of the extended theories is given from the point of view of the mechanistic statistical theory of irreversible processes.     

Normal modes in irreversible thermodynamics

We show that the linear equations of irreversible thermodynamics possess normal mode solutions allowing a simple spectral decomposition of the Green function and of the time-correlation function of thermal fluctuations. In the nondegenerate case it is possible to introduce normal coordinates with exponential behavior in time. As an application we consider the normal mode analysis of damped mechanical systems.     

TheH theorem and irreversible thermodynamics

Following a method first introduced by Prigogine, theH theorem is written as the law of increase of entropy for a slightly inhomogeneous gas. It is shown that the local rate of entropy production for such a gas is simply a homogeneous quadratic form of the generalized forces associated with the various irreversible processes with coefficients possessing all the properties of the phenomenological coefficients of irreversible thermodynamics. The local rate of entropy production is explicitly evaluated for a simple monatomic gas and is compared with the corresponding expression of irreversible thermodynamics.     

The irreversible thermodynamics of black holes

The action of quantum fluctuations of the gravitational field may be regarded as the origin of the dissipative processes associated with Hawking radiation. In this picture the black hole possesses internal coherence by virtue of the localization of its mass. The cumulative effect of the quantum fluctuations in the geometry is that this coherence is corrupted and the mass is sapped away.This essay was awarded the fourth prize for 1977 by the Gravity Research Foundation.     

A kinetic derivation of extended irreversible thermodynamics

The basic postulates of the extended irreversible thermodynamics are derived from the kinetic model for a dilute monoatomic gas. Using the Grad 13-moment method to solve the full nonlinear Boltzmann equation for molecules conceived as soft spheres we obtain the microscopic expressions for the entropy flux, the entropy production, and the generalized Pfaffian for the extended definition of entropy as required by such a theory. Some of the physical implications of these results are discussed.Member, Colegio Nacional.     

The kinetic foundation of extended irreversible thermodynamics revisited

Extended irreversible thermodynamics (EIT) has been used mainly to study the short-time behavior of fluids and some other systems. It has also been shown how the structure of the equations of motion constructed for the so-called relaxation variables coincides with those obtained by means of Grad's method in kinetic theory. In this work we calculate the generalized entropy from the one-particle distribution function up to 26 moments. We find that the characteristics of such entropy and the equations of motion for the relaxing variables are supported by the kinetic theory. This is not the case for the hierarchical relaxation hypothesis which is used in the applications of EIT to the generalized hydrodynamic regime.On temporary leave at the Universidad Iberoamericana, Mexico.     

Effects of spatial variations in extended irreversible thermodynamics

A generalization of extended irreversible thermodynamics is obtained by including the gradients of conserved and nonconserved variables in the space of thermodynamical states. The relaxation equations for these additional state variables are derived systematically from the basic postulates of the theory, for the special case of a rigid heat conductor. Finally, the physical implications of our method are discussed and compared with those of other work on the subject.     

Variational principle for the thermodynamics of irreversible processes

A general variational principle equivalent to the balance equations is considered. Conditions of variation are based on stochastic ideas. A connection between the varied expression and the entropy is derived for both the relativistic case and the nonrelativistic approximation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 47–51, May, 1980.     

Information-theoretic stability and evolution criteria in irreversible thermodynamics

Generalized information gains are used to derive stability conditions, for steady states, periodic orbits and invariant sets, and general evolution criteria, both global and local with respect to the time variable, in irreversible thermodynamics. Meixner's passivity condition and the Glansdorff-Prigogine stability and evolution criteria are found to be special cases thereof. The information gain quantities include Kullback's three kinds of divergences, the first two of which are dual to each other and yield criteria which are symmetric in the average densities of the system's extensive variables and the conjugate parameters, but which are nonsymmetric in the irreversible fluxes and forces, while the third one does not involve the entropy function of the system. Furthermore, Renyi's information gain of order and Csiszar'sf-divergence are treated. The latter is used to construct a most general information gain quantity as a Liapunov function and evolution criterion, which, however, for local stability and evolution conditions is still equivalent to the use of the second-order variation of the entropy.Supported by the Deutsche Forschungsgemeinschaft.     

Comment on Keizer's critique on extended irreversible thermodynamics

Keizer's critique on extended irreversible thermodynamics is responded and qualified so as to remove misleading points of his statements. It is particularly pointed out that contrary to his assertion, fluctuating irreversible thermodynamics may be regarded as being included in extended irreversible thermodynamics as a special case, since it is derivable from the latter when the relaxation times of fluxes are comparatively shorter than the hydrodynamic relaxation time and the initial conditions for the evolution equations are random.Work supported by the grants from the Natural Sciences and Engineering Research Council of Canada.     

Modelling surface rheology of complex interfaces with extended irreversible thermodynamics

The rheological properties of the interfaces in complex multiphase systems often play a crucial role in the dynamic behavior of these systems. For example, these properties affect the dynamics of emulsions, of dispersions of vesicles, of biological fluids, or of free surface flows. In the past three to four decades a vast amount of literature has been produced dealing with the rheological properties of interfaces stabilized by low molecular weight surfactants, proteins, (bio)polymers, lipids, colloidal particles, and various mixtures of these surface active components. The data of these surface rheological experiments are often analyzed with ad hoc generalizations of rheological models used for the analysis of rheological properties of bulk phases. The validity of these generalizations is in general not discussed. Here we show how the extended irreversible thermodynamics (EIT) formalism can be used to generate a wide range of thermodynamically admissible constitutive models for the surface stress tensor, which not only encompass currently used constitutive models, but also suggest several new ones, particularly useful for modelling the nonlinear response of interfaces.