Liliana Restuccia

Mesoscopic transport equations and contemporary thermodynamics: an introduction

The local equilibrium hypothesis is a very successful basis for non-equilibrium thermodynamics over a wide range of phenomena and physical situations. However, the increasing interest in small systems in nanotechnology, in rarefied gases in high-altitude aeronautics, in high-frequency behaviour in information processing, or the search for new materials with sophisticated internal microstructures and tailored thermal properties have led one to ask about the limits of validity of this hypothesis, and to go beyond it. Here we do so in a constructive way, i.e. not only pointing out at these limits, but also embedding the local-equilibrium theory in a more general framework which explicitly exhibits these limits and suggests how to go beyond them, in search for a wider range of applications and a deeper understanding of the foundations.

Asymptotic waves in anelastic media without memory (Maxwell media)

A general method devised to construct oscillatory approximate solutions is applied to a system of equations which describes the behaviour of isotropic media in which mechanical relaxation phenomena occur. The propagation into a uniform unperturbed state is explicitly worked out and the growth equation is established. Finally, the critical time is evaluated.

Non-linear dissipative waves in viscoanelastic media

The propagation of non-linear dissipative waves in viscoanelastic media without memory is considered. By applying an asymptotic perturbative method the transport equation for the first perturbation term is obtained. Finally, it is shown that this equation can be reduced to an equation similar to Burgers equation.

Entropy production in polarizable bodies with internal variables

Abstract A model of polarizable media investigated by Maugin and coworkers is considered as the domain of application of a recent method for the geometrization of the thermo-elasticity of continua with internal variables. The polarization together with its space gradient are assumed as state variables expressed in terms of internal variables evolving according to a relaxation law driven by external and internal electric fields. The entropy productions in Clausius-Duhem inequalities are calculated explicitly.

On generalizations of the Debye equation for dielectric relaxation

In some previous papers one of us (G.A.K.) discussed dielectric relaxation phenomena with the aid of non-equilibrium thermodynamics. In particular the Debye equation for dielectric relaxation in polar liquids was derived. It was also noted that generalizations of the Debye equation may be derived if one assumes that several microscopic phenomena occur which give rise to dielectric relaxation and that the contributions of these microscopic phenomena to the macroscopic polarization may be introduced as vectorial internal degrees of freedom in the entropy. If it is assumed that there are n vectorial internal degrees of freedom an explicit from for the relaxation equation may be derived, provided the developed formalism may be linearized. This relaxation equation has the form of a linear relation among the electric field E, the first n derivatives with respect to time of this field, the polarization vector P and the first n + 1 derivatives with respect to time of P. It is the purpose of the present paper to give full details of the derivations of the above mentioned results. It is also shown in this paper that if a part of the total polarization P is reversible (i.e. if this part does not contribute to the entropy production) the coefficient of the time derivative of order n + 1 of P in the relaxation equation is zero.

The generalized Burgers equation in viscoanelastic media with memory

Abstract In this paper the propagation of non-linear dissipative waves in viscoanelastic media with memory is considered using a thermodynamic theory for mechanical relaxation phenomena proposed in some previous papers. In particular we investigate the contributions of the memory effects on the transport equation which governs the first perturbation term of the asymptotic solution of the basic equation. Finally, it is shown that the transport equation can be reduced to a generalized Burgers equation.

MATERIAL ELEMENT MODEL AND THE GEOMETRY OF THE ENTROPY FORM

In this work we analyze and compare the model of the material (elastic) element and the entropy form developed by Coleman and Owen with that one obtained by localizing the balance equations of the continuum thermodynamics. This comparison allows one to determine the relation between the entropy function S of Coleman–Owen and that one imported from the continuum thermodynamics. We introduce the Extended Thermodynamical Phase Space (ETPS) and realize the energy and entropy balance expressions as 1-forms in this space. This allows us to realizes I and II laws of thermodynamics as conditions on these forms. We study the integrability (closure) conditions of the entropy form for the model of thermoelastic element and for the deformable ferroelectric crystal element. In both cases closure conditions are used to rewrite the dynamical system of the model in term of the entropy form potential and to determine the constitutive relations among the dynamical variables of the model. In a related study (to be published) these results will be used for the formulation of the dynamical model of a material element in the contact thermodynamical phase space of Caratheodory and Hermann similar to that of homogeneous thermodynamics.

On a thermodynamic theory for magnetic relaxation phenomena due to n microscopic phenomena described by n internal variables

Abstract In this paper a theory for magnetic relaxation phenomena developed in the framework of thermodynamics of irreversible processes (TIP) with internal variables by G. A. Kluitenberg (G.A.K.) and the author is reviewed. Analogies and correlations with thermodynamic theories with internal variables for mechanical distortional phenomena and dielectric relaxation phenomena, derived, respectively, by G. A. K., and by G. A. K. and the author, following the same procedure, are put forward as evidence. It is assumed that if n different types of irreversible microscopic phenomena give rise to magnetic relaxation, it is possible to describe these microscopic phenomena splitting the total specific magnetization in n + 1 parts and introducing n of these partial specific magnetizations as internal variables in the thermodynamic state space. The phenomenological equations are formulated in the anisotropic and isotropic cases. Finally, linearizing the equations of state, generalizations of the Snoek equation for magnetic relaxation phenomena are obtained by eliminating the internal variables. Some results obtained in the paper are new.

Diffusion and dislocation influences on the dynamics of elastic bodies

Abstract A nonconventional model based on the extended irreversible thermodynamics of physical processes in which the diffusion of mass and the dislocation field interact in an elastic body is presented. The theory is applied to a case of diffusion-dislocation interactions with the defective body forced by a periodic subcritical stress which admits the relaxation character of the diffusion and dislocation fields.

On the invariance of Onsager's reciprocal relations in the thermodynamic theory of dielectric relaxation phenomena

In some previous papers a theory for dielectric relaxation phenomena in polarizable media was developed by introducing a set of thermodynamic internal variables identified with the n + 1 partial specific polarization vectors p(k) (k = 0, 1, 2, …, n) in which the total specific polarization vector p can be split. Moreover, it was shown that the entropy production can be characterized also if a set of n “hidden” vectorial parameters Z(λ) (k = 1, 2, …, n), related to the p(k) (k = 1, 2, …, n) by vector-valued transformation laws, is assumed as new thermodynamic variables. Of course two forms for the balance equation for the entropy can be deduced and two formalisms for the development of the theory can be derived. In the present paper we point out that these two formalisms are equivalent and we show that the corresponding Onsager reciprocal relations for the phenomenological coefficients are invariant under the vector-valued transformations between the two sets of internal variables.