Resumo Os Sistemas Dinâmicos Complexos são sistemas com propriedades emergentes inesperadas resultantes de processos sinérgicos de seus componentes. Estes sistemas aparecem na física e na química e desempenham um papel fundamental em sistemas biológicos. Tais sistemas requerem um tratamento teórico em termos de “Modelagem Matemática”, com os formalismos estatísticos sendo de grande relevância. Apresentamos aqui um artigo explanatório descrevendo e discutindo o tema. Apresentamos uma revisão do assunto com particular atenção à Teoria da Informação em uma abordagem de Shannon-Jaynes no espírito da proposta de inferência científica de Jeffreys. Enfatiza-se a difícil questão da presença das “hidden constraints” e a introdução de estatísticas não convencionais que surgem no âmbito da “Teoria da Informação”.

Abstract The “Complex Dynamical Systems” are systems with unexpected emerging properties which are the result of synergetic processes of their components. These systems appear in condensed matter physics and chemistry, as well as, playing a fundamental role, in biological systems. They require a theoretical treatment in terms of “Mathematical Modelling”, with statistical formalisms being of large relevance. We present here a feature-like article describing and discussing the question. Particular attention has been done on the basis of Information Theory in a Shannon-Jaynes approach in the spirit of Jeffreys' scientific inference proposal. It is emphasized the difficult question of presence of “hidden constraints”, and the introduction of nonstandard statistics arising in the realm of “Information Theory”.

The nowadays notable development of all the modern technology, fundamental for the progress and well being of world society, imposes a great deal of stress in the realm of basic Physics, more precisely on Thermo-Mechanical Statistics. In electronics and optoelectronics we face situations involving physical-chemical systems far-removed-from equilibrium, where ultrafast (in pico- and femto-second scale) and non-linear processes are present. Here we describe in an extended overview the question of ultrafast relaxation processes in the excited plasma in semiconductors.

<p>Neste artigo consideramos os aspectos gerais dos temas emergentes na segunda metade do século passado, de complexidade, auto-organização e informação. Os três estão ligados pelo fato de estarem envolvidos na “teoria de sistemas dinâmicos”, e sobre esse ponto enfocamos a descrição aqui apresentada. Descreve-se o surgimento de comportamento complexo em tais sistemas dinâmicos em geral quando governados por uma teoria cinética não linear, a emergência de estruturas dissipativas sinergéticas à la Prigogine-Haken, e a teoria de informação via o enfoque de inferência científica proposto por Jeffreys-Jaynes.</p>

<p>We describe certain general aspects of the topics complexity, self-organization and information, which emerged during the second half of the last century. They are entailed to the “theory of dynamical systems”, and it is from such point that we focus the description here presented. We describe how complex behavior arises in dynamical systems in general when they are governed by a non-linear kinetic theory as well as the emergence of self-organized structures (in the sense of the synergetic self-organized dissipative structures ”à la Prigogine-Haken”), and the theory of information through the point of view of the scientific inference of Jeffreys-Jaynes.</p>

The nowadays notable development of all the modern technology, fundamental for the progress and well being of world society, imposes a great deal of stress in the realm of basic Physics, more precisely on Thermo-Statistics. We do face situations in electronics and optoelectronics involving physical-chemical systems far-removed-from equilibrium, where ultrafast (in pico- and femto-second scale) and non-linear processes are present. Further, we need to be aware of the rapid unfolding of nano-technologies and use of low-dimensional systems (e.g., nanometric quantum wells and quantum dots in semiconductor heterostructures). All together this demands having an access to a Statistical Mechanics being efficient to deal with such requirements. It is worth noticing that the renowned Ryogo Kubo once stated that "statistical mechanics has been considered a theoretical endeavor. However, statistical mechanics exists for the sake of the real world, not for fictions. Further progress can only be hoped by close cooperation with experiment". Moreover, one needs to face the study of soft matter and fluids with complex structures (usually of the average self-affine fractal-like type). This is relevant for technological improvement in industries like, for example, that of polymers, petroleum, cosmetics, food, electronics and photonics (conducting polymers and glasses), in medical engineering, etc. It is then required to introduce a thermo-hydrodynamics going well beyond the classical (Onsagerian) one. Moreover, in the both type of situations above mentioned there often appear difficulties of description and objectivity (existence of so-called "hidden constraints"), which impair the proper application of the conventional ensemble approach used in the general, logically and physically sound, and well established Boltzmann-Gibbs statistics. A tentative to partially overcome such difficulties consists in resorting to non-conventional approaches. Here we briefly describe the construction of a Non-Equilibrium Statistical Ensemble Formalism (NESEF) that can deal, within a certain degree of success, with the situations above described. Several particular instances involving experimental observations and measurements in the area of semiconductor physics and in physics of fluids, which were analyzed in the context of the theory, are summarized. They comprise the cases of ultrafast optical spectroscopy; optical and transport processes in low-dimensional complex semiconductors; nonlinear transport in doped highly-polar semiconductors (of use in "blue diodes") under moderate to high electric fields; nonlinear higher-order thermo-hydrodynamics in fluids under driven flow, in normal solutions and in complex situations as in solutions of polymers, micelles, DNA, and in microbatteries.

A theoretical study of the mobility of n-doped III-Nitrides in wurtzite phase is reported. We have determined the nonequilibrium thermodynamic state of the bulk n-InN, n-GaN, and n-AlN systems - driven far away from equilibrium by a strong electric field - in the steady state, which follows after a very fast transient. For this we solve the set of coupled nonlinear integro-differential equations of evolution of the nonequilibrium thermodynamic variables, for the three materials, to obtain their steady state values. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength and the concentration (of electrons and impurities) is derived, which decreases with the increase of the electric field strength and the concentration of carriers, evidencing the influence of the nonlinear transport involved.

The area of Physics indicated in the title is nowadays of quite relevant interest, not only from the purely scientific point of view, but specially for its applied aspects associated to the present-time point-first-technologies. A particular research trend in the theory of irreversible processes, which are evolving in time in systems arbitrarily departed from equilibrium, is here briefly described. It consists in the construction of a Gibbs-style nonequilibrium ensemble formalism. The derivation of a nonequilibrium statistical operator is described (the variational approach of Predictive Statistical Mechanics is used). The main questions involved are presented and applications are briefly mentioned.

It is reviewed what can be considered as the present research trends in what regards to the construction of an ensemble formalism - Gibbs' style - for the case of far-from-equilibrium systems. The main questions involved are presented accompanied with brief discussions. The construction of a nonequilibrium statistical operator is described and its applications commented, and, particularly, it is presented the derivation of an Irreversible Thermodynamics based on the statistical foundations that the nonequilibrium ensemble formalism provides.

Systems Biology (system-level understanding in biological science), from the physical-chemical point of view, is involved with irreversible thermodynamics and nonlinear kinetic theory of open systems which are founded on nonequilibrium statistical mechanics. We describe a modern thermo-statistical approach for dealing with complex systems, in particular biological systems. We consider the case of a very peculiar complex behavior in open boson systems sufficiently away, from equilibrium, which appear to have large relevance in the functioning of biological systems. This is, on the one hand, the so-called Frohlich-Bose-Einstein-like condensation leading in steady-state conditions to the emergence of a particular case of quantum-large-scale coherent ordering, of the type of a selforganizing-synergetic dissipative structure. Moreover, additional complexity emerges in the form of propagation, in this condensate, of signals (information) consisting of nearly undamped and undistorted, long-distance propagating, solitary waves (the pseudoparticle soliton). It can be accompanied by a so-called Frohlich-Cherenkov cone of emission of polar vibrations, and it is also possible the formation of ¨ metastable states of the form of the so-called bioelectrets. These are phenomena apparently working in biological processes, which are presently gaining relevant status on the basis of eventually providing a large-scale quantum-coherent behavior in cytoskeletons of neurons and the conscious (non-computational) activity in the brain. Emphasis is centered on the quantum-mechanical-statistical irreversible thermodynamics of these open systems, and the informational characteristics of the phenomena. Ways for their experimental evidencing are pointed out and discussed.

Research in ultrasonography has evidenced the propagation of a peculiar kind of excitation in fluids. Such excitation, dubbed a X-wave, has characteristics resembling that of a solitary-wave type. We reconsider the problem in a medium consisting of a biological material of the like of alpha-helix proteins. It can be shown that in this case is expected an excitation of the Davydov's solitary wave type, however strongly damped in normal conditions. The case of acetanilide, an organic polymer which resembles biopolymers, is considered, and the infrared spectrum analyzed. Davydov's soliton is evidenced as a coherent state of polar vibrations. The case of acoustic (sound) vibrations is also considered, where, also, a damped Davydov-like solitary wave may be excited. However, it is shown that when traveling in conditions sufficiently away from equilibrium, more precisely, when the soliton is embeded in the resulting Frohlich-Bose-Einstein condensate, the lifetime of the solitary wave is largely enhanced. Moreover, a soliton moving in bulk with a velocity larger than that of the group velocity of the normal vibrational waves would produce a Cherenkov-like emission of phonons giving rise to the observed X-wave-like pattern. This paper is a modified and extended version of an earlier publication on the subject.

A study of the mobility of n-doped wurtzite III-Nitrides is reported. We have determined the nonequilibrium thermodynamic state of the III-Nitrides systems driven far away from equilibrium by a strong electric field in the steady state, which follows after a very fast transient. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength is derived, which decreases with the strength of electric field. We analyzed the contributions to the mobility arising out of the different channels of electron scattering, namely, the polar optic, deformation, piezoelectric, interactions with the phonons, and with impurities. The case of n-InN, n-GaN, and n-AlN have been analyzed: as expected the main contribution comes from the polar-optic interactions in these strongly polar semiconductors. The other interactions are in decreasing order, the deformation acoustic, the piezoelectric, and the one due to impurities.

We contribute here a theoretical study of the electron mobility in n-doped GaN, InN, and AlN at moderate to high electric fields. We solve the set of coupled nonlinear integro-differential equations of evolution to obtain the steady-state values of the basic intensive nonequilibrium thermodynamic variables for the three materials. The regions with ohmic and non-ohmic behavior in the electron drift velocity dependence on the electric field strength are characterized in the three nitrides. The electron mobility is calculated, and it is shown that the larger corresponds to InN, and the smaller to AlN.

Several aspects of the Thermodynamics of systems away from equilibrium are considered. Particular attention is given to the question of the concepts of entropy and temperature in arbitrary nonequilibrium conditions. Even though such state function and thermodynamic variable are elusive in such conditions, it is elaborated and discussed an approach to them that can be obtained in the framework of the so-called Informational Statistical Thermodynamics. This is the approach to Thermodynamics based on the statistical-mechanical foundations provided by a Gibbs ensemble-like algorithm in nonequilibrium situations. The resulting nonequilibrium temperature-like variable - dubbed as quasitemperature - is shown to be a quantity measurable with appropriate "thermometric devices". A comparison of quasitemperatures that arise in different approximated nonequilibrium statistical-thermodynamic descriptions of the dissipative system is done. The validity of these different approximations is evaluated, and (in the framework of the theory) generalized Gibbs, Clausius, and Boltzmann's relations, as well as properties of the corresponding entropy-like function (or informational entropy in Jaynes-Shannon sense), that the theory introduces, are presented. Conceptual and physical aspects of the question are also discussed, and a partial comparison of these concepts with those arising in other approaches to irreversible thermodynamics is briefly attempted. This article is an enlargement of a paper in Fortschritte der Physik/Progress of Physics, 47, 9 (1999), where have been added extensive comments on the subject.

We reconsider a nonlinear quantum kinetic theory which is built within the context of a nonequilibrium statistical ensemble formalism. This is the Nonequilibrium Statistical Operator Method based on a variational principle, namely, the Maximization of the Informational-Statistical Entropy, and referred to as MaxEnt-NESOM. It may be considered as encompassed within the framework of E. T. Jaynes' Predictive Statistical Mechanics. These theory has an ample domain of application covering a large class of experimental conditions. We consider a particular <FONT FACE="Symbol">¾</font> and quite important <FONT FACE="Symbol">¾</font> limiting case, consisting in the Markovian approximation. For illustration we applied it to the study of a spin system in interaction with the lattice. The presentation is an extended and detailed version of a Brief Report published in Phys. Rev. E 57, 3637-3640 (1998).

It is shown how the closure condition for the set of kinetic equations in Zubarev's Nonequilibrium Statistical Operator Method introduces a series of fluxes of a reference set of densities. These fluxes are the average values, over a Gibbs-like nonequilibrium generalized grand-canonical ensemble, of Hermitian operators for fluxes defined at the microscopic-mechanical level. The equations of evolution for these fluxes (or equivalently for their conjugated Lagrange multipliers) are described.