Patrizia Rogolino

A GEOMETRIC PERSPECTIVE ON IRREVERSIBLE THERMODYNAMICS WITH INTERNAL VARIABLES

The thermodynamics of simple materials is analysed from a geometrical point of view. The model provides a suitable framework for dissipative structures arising during the evolution of the system.

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.

A mesoscopic approach to diffusion phenomena in mixtures

Abstract The mesoscopic concept is applied to the theory of mixtures. The aim is to investigate the diusion phenomenon from a mesoscopic point of view. The domain of the field quantities is extended by the set of mesoscopic variables, here the velocities of the components. Balance equations on this enlarged space are the equations of motion for the mesoscopic fields. Moreover, local distribution functions of the velocities are introduced as a statistical element, and an equation of motion for this distribution function is derived. From this equation of motion, dierential equations for the diusion fluxes and also for higher order fluxes are obtained. These equations are of balance type, as it is postulated in extended thermodynamics. The resulting evolution equation for the diusion flux generalizes Ficks law.

Thermodynamic Transformations in Magnetically Polarizable Undeformable Media

Abstract In this paper the problem of magnetically undeformable polarizable media in the presence of an electromagnetic field is analyzed from a thermodynamic viewpoint. The thermodynamic transformations are explicited as functions in the state space in which one of the variables, characterizing the magnetic polarization, is given as an internal variable. The entropy form along the thermodynamic transformation is calculated for para- and diamagnetic media and the necessary conditions for its existence are given.

On the Mathematical Structure of Thermodynamics with Internal Variables

Abstract The mathematical properties of thermodynamics with internal variables are investigated in a general framework, both for the local and gradient theory. The consequences of the Second Law of Thermodynamics on the constitutive equations, together with some peculiar properties of the equilibrium states, are proved. The evolution equations of the internal variables are derived as a system of Hamilton equations resulting from a suitable Legendres transformation.

Constitutive Equations for Internal Variables Thermodynamics of Suspensions

Abstract A description of mixtures, including matter diffusion and suspensions, is analyzed from a thermodynamic viewpoint with internal variables. In order to consider dissipative effects due to thermo-diffusion we introduce a set of N independent scalar internal variables, which we denote by γA . The behavior of the mixture is therefore described by a state space W including the classical variables mass density, mass concentration, temperature, and internal variables together with their first and second gradients satisfying evolution equations. General thermodynamic restrictions and residual dissipation inequalities are obtained by the Clausius–Duhem inequality.

Internal Variables Thermodynamics of Two Component Mixtures under Linear Constitutive Hypothesis with an Application to Superfluid Helium

Abstract A model of binary mixtures with an application to superfluid helium is analyzed from a thermodynamical viewpoint with internal variables. Constitutive equations under hypotheses of linearity are obtained.

Thermodynamics of Mixtures as a Problem with Internal Variables. The General Theory

Abstract A model of a mixture with N different components is analyzed from a thermodynamic viewpoint with internal variables, both in the presence and absence of viscosity. Thermodiffusion phenomena are described by N internal variables (N ≥ 2). General thermodynamic restrictions and residual dissipation inequalities are obtained by the Clausius–Duhem inequality.

Generalized heat-transport equations: parabolic and hyperbolic models

We derive two different generalized heat-transport equations: the most general one, of the first order in time and second order in space, encompasses some well-known heat equations and describes the hyperbolic regime in the absence of nonlocal effects. Another, less general, of the second order in time and fourth order in space, is able to describe hyperbolic heat conduction also in the presence of nonlocal effects. We investigate the thermodynamic compatibility of both models by applying some generalizations of the classical Liu and Coleman–Noll procedures. In both cases, constitutive equations for the entropy and for the entropy flux are obtained. For the second model, we consider a heat-transport equation which includes nonlocal terms and study the resulting set of balance laws, proving that the corresponding thermal perturbations propagate with finite speed.

Minimal Entropy Production and Efficiency of Energy Conversion in Nonlinear Thermoelectric Systems with Two Temperatures

Abstract In this paper we determine the physical conditions ensuring that the efficiency of a thermoelectric nanowire with two temperatures is optimal. We consider the case in which the entropy for unitary volume depends on the equilibrium variables only, and the case in which such a quantity depends on the dissipative fluxes, too. We prove that in these two different situations the conditions of optimal efficiency are different.