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.     

Response to Z. Banach's comments on the modified moment method and irreversible thermodynamics

In this paper the author responds to the comments on the modified moment method and irreversible thermodynamics made by Z. Banach [Physica A 145 (1987) 105]. In this paper Banach suggests a variational method in which the Lagrange multipliers are determined from the constraints alone by disregarding the entropy balance equation. It is shown that since this method does not yield an extended Gibbs relation consistent with the entropy balance equation or the H-theorem, there is no irreversible thermodynamics formalism afforded by the method. Consequently, his criticism cannot be supported from the viewpoint of irreversible thermodynamics. It is also pointed out that neither is there a mathematical and physical support for the criticism he makes on the cumulant expansion for the Boltzmann collision integral.     

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.     

Escape-Rate Formalism, Decay to Steady States, and Divergences in the Entropy-Production Rate

According to thermodynamics the irreversible entropy production of diffusive relaxation processes diverges at the boundary to the vacuum, i.e., to a state of vanishing particle density. By means of a multibaker map we point out that this divergence is not present in the spatially discrete dynamics, which brings forth the evolution equations of irreversible thermodynamics in the continuum limit. In addition, we show that the irreversible entropy production of relaxation towards a nonempty steady state is proportional to the decay rate of the thermodynamic system subjected to absorbing boundary conditions. This generalizes results of the escape rate formalism.     

Dual-phase-lag transfer equations and entropy behavior in relaxational hydrodynamics

Extended thermodynamics of irreversible processes is developed; based on two postulates by which additional variables of the entropy density are dissipative fluxes and material time derivatives of the ordinary thermodynamic variables. Within these theories a more general approximation of entropy production is obtained. As a consequence of the proposed formalism, the constitutive dual-phase-lag equations, as well as equations of the conventional version of extended irreversible thermodynamics are obtained. The behavior of the entropy during oscillatory approach to equilibrium is considered. The proposed theory leads to a strictly monotonic dependency of the entropy on time.     

Theorie der Multipolrelaxation

The multipole resonance and relaxation is discussed starting with a general consideration of the quantum mechanical dynamics of spinsystems with arbitrary spinI. The irreversible entropy production as a function of the multipolarisations is calculated from the density operator, expanded in terms of a complete set of orthonormal multipole operators. By use of the methods of thermodynamics of irreversible processes one obtains relaxation equations, which are a generalization of the Bloch equations of pure magnetic dipole relaxation. They connect the time derivatives of the multipolarisations with affinities, which are defined by the expansion of the logarithmus of the density operator; for small multipolarisations the affinities are equal to the multipolarisations themselves. Relations for the relaxation matrix are discussed, especially a derivation is given for reciprocal relations between the relaxation coefficients. In the special case of spinI=1 the equations of quadrupole relaxation are studied for axial symmetry.     

Local nonequilibrium mass transfer in a two-component system under external pulsed irradiation with energy fluxes

The nonisothermal mass transfer in metal materials under irradiation with concentrated energy fluxes is studied in the one-dimensional approximation. Local nonequilibrium equations of extended irreversible thermodynamics are used to describe the transfer phenomena. It is established that, for short times (on the order of the time required for relaxation of the diffusion flow to its local-equilibrium value), the wave mechanism for mass transfer is dominant over the diffusion one, ensuring that the impurity-concentration profiles have a nonmonotonous form. The degree of influence of the space-time nonlocality of the transfer processes on the formation of concentration profiles is estimated, and the model results are compared with the experimental data.     

Modeling interfacial dynamics using nonequilibrium thermodynamics frameworks

In recent years several nonequilibrium thermodynamic frameworks have been developed capable of describing the dynamics of multiphase systems with complex microstructured interfaces. In this paper we present an overview of these frameworks. We will discuss interfacial dynamics in the context of the classical irreversible thermodynamics, extended irreversible thermodynamics, extended rational thermodynamics, and GENERIC framework, and compare the advantages and disadvantages of these frameworks.     

Foundation of quasilinear irreversible thermodynamics

In the set of axioms of the linear thermodynamics of irreversible processes the linearity law is replaced by a more general relation (8) coupling fluxes and forces and their time derivatives. It is shown that the remaining axioms of the classical irreversible thermodynamics (OnsagerCasimir relations and the entropy production expression) can be left unchanged. It is derived that in the frame of this theory it is possible to picture the Maxwell model of viscoelastic effects and the Debye model of the dielectric relaxation.     

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.     

Thermodynamics of a continuous medium with electric and magnetic dipoles

The thermodynamics of an electrically charged, multicomponent fluid with spontaneous electric and magnetic dipoles is analysed in the presence of electromagnetic fields. Taking into account the chemical composition of the current densities and stress tensors leads to three types of irreversible terms: scalars, vectors and pseudo-vectors. The scalar terms account for chemical reactivities, the vectorial terms account for transport and the pseudo-vectorial terms account for relaxation. The linear phenomenological relations, derived from the irreversible evolution, describe notably the Lehmann and electric Lehmann effects, the Debye relaxation of polar molecules and the Landau-Lifshitz relaxation of the magnetisation. This formalism accounts for the thermal and electric magnetisation accumulations and magnetisation waves. It also predicts that a temperature gradient affects the dynamics of magnetic vortices and drives magnetisation waves.     

Irreversible thermodynamics of fluids

Irreversible thermodynamics of fluids is formulated based on a set of postulates. The theory thus constructed generalizes thermostatics and linear irreversible thermodynamics into the realm of nonlinear irreversible processes. In this theory the extended Gibbs relation and the entropy balance equation appear as a pair of mutually consistent equations under the postulates made. An equivalent theory is also formulated by replacing one of the postulates with another that is basically a variational principle. The variational principle yields the evolution equations for fluxes as the Euler equations that extremize the variational functional postulated. The local form of the extremized variational functional is the entropy balance equation for the irreversible processes in the system. Some further consequences of the theory are also considered. For example, nonequilibrium specific heats are shown to be at least quadratic functions of fluxes and reduce to the equilibrium specific heats in the limit of vanishing fluxes. In order to illustrate an example of possible applications, we have considered nonlinear transport processes in fluids. The connections of the present theory with other theories are discussed.     

Diffusion in multicomponent systems

Some consequences of the thermodynamics of irreversible processes on the diffusion coefficients are discussed. The corresponding inequalities for the diffusion coefficients are derived.Dedicated to Professor Miroslav Trlifaj on the occasion of his sixtieth birthday.     

Generalized thermodynamic stability of systems under shear

Starting from the extended irreversible thermodynamics (EIT) theory, some corrections to the specific heat and to the thermal compressibility of a nonequilibrium system are obtained. We study the subsequent modifications of the static stability conditions of a system under shear. In some situations, a shear-induced melting transition can be present.     

On the molecular sound absorption in fluid mixtures

Measurements of sound absorption in binary mixtures of gases in which two relaxation processes can occur due to the specific heats of the molecular vibrations, have hitherto been evaluated by using a theory based mainly on gaskinetic considerations. The theory presented here, uses the thermodynamics of irreversible processes as developed byMeixner for sound absorption in fluid systems due to interior reactions of arbitrary kind and number. This treatment permits a concise derivation of the final formulas which are also valid for mixtures of real gases and fluids. According to which set of independent thermodynamical variables for the derivation is used, the final formulas seem to differ considerably. It is pointed out that these differences arise from introducing two types of relaxation times and may be eliminated by means of the relationship between these relaxation times.     

Magnetic relaxation in a spin-1 Ising model near the second-order phase transition point

The magnetic relaxation of a spin-1 Ising model with bilinear and biquadratic interactions is formulated within the framework of statistical equilibrium theory and the thermodynamics of irreversible processes. Using a molecular-field expression for the magnetic Gibbs energy, the magnetic Gibbs energy produced in the irreversible process is calculated and time derivatives of the dipolar and quadrupolar order parameters are treated as fluxes conjugate to their appropriate generalized forces in the sense of Onsager theory. The kinetic equations are obtained by introducing kinetic coefficients that satisfy the Onsager relation. By solving these equations an expression is derived for the dynamic or complex magnetic susceptibility. From the real and imaginary parts of this expression, magnetic dispersion and absorption factor are calculated and analyzed near the second-order phase transition.