L. S. Garcia-Colin

The Kinetic Foundations 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 Grads 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 the nature of the so-called generic instabilities in dissipative relativistic hydrodynamics

It is shown that the so-called generic instabilities that appear in the framework of relativistic linear irreversible thermodynamics (LIT), describing the fluctuations of a simple fluid close to equilibrium, arise due to the coupling of heat with hydrodynamic acceleration which appears in Eckart’s formalism of relativistic irreversible thermodynamics. Further, we emphasize that such behavior should be interpreted as a contradiction to the postulates of LIT, namely a violation of Onsager’s hypothesis on the regression of fluctuations, and not as fluid instabilities. Such contradictions can be avoided within a relativistic linear framework if a Meixner-like approach to the phenomenological equations is employed.

A unified approach for deriving kinetic equations in nonequilibrium statistical mechanics. I. Exact results

A unified method for deriving exact kinetic equations for dynamical quantities of a many-body system is presented. The well-known results of Mori and Zwanzig are recovered as special cases. Furthermore, it is shown that they differ only by the way in which the system is prepared at the initial time. Connections between this method and others recently developed are also discussed.

Relativistic non-equilibrium thermodynamics revisited

Abstract Relativistic irreversible thermodynamics is reformulated following the conventional approach proposed by Meixner in the non-relativistic case. Clear separation between mechanical and non-mechanical energy fluxes is made. The resulting equations for the entropy production and the local internal energy have the same structure as the non-relativistic ones. Assuming linear constitutive laws, it is shown that consistency is obtained both with the laws of thermodynamics and causality.

Entropy Production: Its Role in Non-Equilibrium Thermodynamics

It is unquestionable that the concept of entropy has played an essential role both in the physical and biological sciences. However, the entropy production, crucial to the second law, has also other features not clearly conceived. We all know that the main difficulty is concerned with its quantification in non-equilibrium processes and consequently its value for some specific cases is limited. In this work we will review the ideas behind the entropy production concept and we will give some insights about its relevance.

Diffusion and mobility and generalized Einstein relation

The general response theory to thermal perturbations presented in the preceding paper is applied to a simple model. We obtain the evolution equation for the particle density, which becomes of the form of a propagating wave with a damping dependent on the diffusion coefficient. The latter is calculated at the microscopic level. For a charged system we also determine the mobility coefficient for arbitrarily intense electric fields, obtaining a generalized Ohms law for nonlinear charge transport. Using the expressions for both transport coefficients we derive the Einstein relation in the nonlinear nonequilibrium thermodynamic state of the system.

Relativistic transport theory for simple fluids to first order in the gradients

In this paper we show how using a relativistic kinetic equation the ensuing expression for the heat flux can be cast in the form required by Classical Irreversible Thermodynamics. Indeed, it is linearly related to the temperature and number density gradients and not to the acceleration as the so called “first order in the gradients” theories propose. Since the specific expressions for the transport coefficients are irrelevant for our purposes, the BGK form of the kinetic equation is used. Moreover, from the resulting hydrodynamic equations it is readily seen that the equilibrium state is stable in the presence of the spontaneous fluctuations in the transverse hydrodynamic velocity mode of the simple relativistic fluid. The implications of this result are thoroughly discussed.

Generalization of the Williams–Landel–Ferry equation

Based on the model of Gibbs–Di Marzio we write the logarithmic shift factor without explicit knowledge of the form for the entropy, an expression which enables us to write a generalization of the Williams–Landel–Ferry equation. Comparison with the empirical relation of Williams–Landel–Ferry and use of the fact that the model exhibits the existence of a isoentropic temperature T0 for which the configurational entropy of the system vanishes, leads to a value of the isoentropic temperature for which the configurational entropy of the system vanishes. The form for the specific heat proposed by Dowell and Di Marzio based on the lattice model of Gibbs–Di Marzio for the glass transition of polymeric substances, has been used by Garcia-Colin et al. to find the molar configurational entropy (MCE) of glass. Knowledge of the form of the MCE, allows us to find an expression for the critical configurational entropy (Sc∗) and a form for the potential energy hindering the cooperative rearrangement per monomer segment (Δμ).

The foundations of informational statistical thermodynamics revisited

The aim of this paper is to review the fundamental ideas of the underlying method behind informational statistical thermodynamics. This method is set forth to deal with phenomena that occur in nonequilibrium systems. The most significant aspects of this analysis are: 1.(i) To show that Abels theorem guarantees that in the asymptotic limit, the nonequilibrium statistical operator (NSO) obtained by MAXENT generates a stationary solution of the Liouville equation. This fact is consistent with the experimental behavior of an equilibrium system.2.(ii) Further, it is also shown how a Liouville equation with sources can be obtained by the NSO determined by MAXENT, whose formal solution proves that the general interpretation of Abels theorem leading to memory effects is incorrect. Rather, this theorem introduces a time smoothing function in a time interval: t0 = −∞ < t′ < t1 (t1: initial time of an observation), which is to be understood as one that connects an adiabatic perturbation for t′ < t1. In fact, the memory effects appear in the evolution equations for the average values of the dynamical variables obtained by the NSO when these evolution equations are calculated up to second order in the perturbation Hamiltonian.3.(iii) Also, some criticisms that have been presented against MAXENT formalism are discussed and it is shown that they are inapplicable. Such criticisms are related to the memory effects and with the inconsistency of evolution equations for macrovariables with respect to the total energy conservation equation.

Response function theory for thermal perturbations in informational statistical thermodynamics

In the context of a microscopic approach to phenomenological irreversible thermodynamics, based upon nonequilibrium mechano-statistical foundations, we consider here questions related to the response of many-body nonequilibrium systems to thermal perturbations arising out of inhomogenities in the medium. We present a general theory of the resulting transport phenomena which is nonlocal in space and memory dependent. The limit of the local in space and instantaneous in time approximations is also considered and discussed. Propagation of damped waves is evidenced in equations of the Maxwell-Cattaneo type, which are generalizations of the diffusion-like equations of classical irreversible thermodynamics. A particular example of application of the theory is presented in the follow up article.