1,721,001 research outputs found
Derivation In A Nonequilibrium Ensemble Formalism Of A Far-reaching Generalization Of A Quantum Boltzmann Theory
No full textWithin the framework of the nonequilibrium statistical ensemble formalism provided by the nonequilibrium statistical operator method, we derive a quantum Boltzmann-style transport theory of a broad scope. This is done by choosing the single- and two-particle dynamical density operators as the basic informational-statistical variables. The equations of evolution for their average values over the nonequilibrium ensemble, the nonequilibrium-reduced Dirac-Landau-Bogoliubov-type density matrices, are obtained. From the resulting generalized nonlinear quantum transport theory, after resorting to perturbative-like expansions, a far-reaching generalization of Boltzmann equation for the single-particle distribution function is derived. A type of traditional Boltzmann equation follows after using stringent approximations, whose limits of validity are evaluated.2841140160Lebowitz, L.L., Montroll, E.W., (1983) Studies in Statistical Mechanics X. Nonequilibrium Phenomena I: the Boltzmann Equation, , North-Holland, AmsterdamJaynes, E.T., (1986) Frontiers of Nonequilibrium Statistical Physics, pp. 33-55. , G.T. Moore, M.O. Scully (Eds.), Plenum, New YorkLuzzi, R., Vasconcellos, A.R., (1990) Fortschr. Phys./Prog. Phys., 38, p. 887Luzzi, R., Vasconcellos, A.R., Ramos, J.G., A Non-equilibrium Statistical Ensemble Formalism: Basic Concepts, Construction, Application, Open Questions and Criticism, , http://xxx.lanl.gov/cond-mat/9909160Zubarev, D.N., (1974) Nonequilibrium Statistical Thermodynamics, Consultants Bureau, , New York, Neravnovesnaia Statisticheskaia Termodinamika, Izd. Nauka, Moscow, 1971Zubarev, D.N., (1970) Fortschr. Phys./Prog. Phys., 18, p. 125Zubarev, D.N., Morozov, V.N., Röpke, G., (1996) Statistical Mechanics of Nonequilibrium Processes, Vol. 1: Basic Concepts, Kinetic Theory, 1. , Akademie Verlag, BerlinZubarev, D.N., Morosov, V., Röpke, G., (1997) Statistical Mechanics of Nonequilibrium Processes Vol. 2: Relaxation and Hydrodynamic Processes, 2. , Akademie Verlag, BerlinAlgarte, A.C., Vasconcellos, A.R., (1992) R. Luzzi, Phys. Stat. Sol. (B), 173, p. 487Mesquita, M.V., Vasconcellos, A.R., Luzzi, R., (1998) Phys. Rev. Lett., 80, p. 2008Madureira, J.R., Vasconcellos, A.R., Luzzi, R., (1998) J. Chem. Phys., 108, p. 7568Madureira, J.R., Vasconcellos, A.R., Luzzi, R., Casas-Vázquez, J., Jou, D., (1998) J. Chem. Phys., 108, p. 7580Bogoliubov, N.N., (1967) Lectures in Quantum Statistics, 1-2. , Gordon and Breach, New York respectivelyFano, U., (1957) Rev. Mod. Phys., 29, p. 74Lauck, L., Vasconcellos, A.R., Luzzi, R., (1990) Physica A, 168, p. 789Akhiezer, A.I., Peletminskii, S.V., (1981) Methods of Statistical Physics, , Pergamon, OxfordLuzzi, R., Vasconcellos, A.R., Ramos, J.G., Foundations of a nonequilibrium ensemble formalism Fundamental Theories of Physics Series, , A. van. der Merwe (Ed.), Kluwer Academic, Dordrecht, forthcomingBogoliubov, N.N., (1962) Studies in Statistical Mechanics I, , J. de Boer, G.E. Uhlenbeck (Eds.), North-Holland, AmsterdamLuzzi, R., Vasconcellos, A.R., Ramos, J.G., Statistical foundations of irreversible thermodynamics Texte Zur Physik Series, , W. Ebeling (Ed.), Teubner, Leipzig, in pressTenan, M.A., Vasconcellos, A.R., Luzzi, R., (1997) Forstchr. Phys./Prog. Phys., 47, p. 1Luzzi, R., Vasconcellos, A.R., Ramos, J.G., (1999) Fortschr. Phys./Prog. Phys., 47, p. 401Madureira, J., Vasconcellos, A., Luzzi, R., Lauck, L., (1998) Phys. Rev. E, 57, p. 3637Vasconcellos, A.R., Algarte, A.C., Luzzi, R., (1990) Physica A, 166, p. 517Huang, K., (1963) Statistical Mechanics, , Wiley, New York, 2nd enlarged Edition, 1987Kreuzer, H.J., (1981) Nonequilibrium Thermodynamics and Its Statistical Foundations, , Clarendon, OxfordLiboff, R.L., (1990) Kinetic Theory, , Prentice-Hall, Englewood Cliffs, NJBalescu, R., (1975) Equilibrium and Nonequilibrium Statistical Mechanics, , Wiley-Interscience, New YorkHeims, S.P., Jaynes, E.T., (1962) Rev. Mod. Phys., 34, p. 143. , subsection b, pp. 148-150, and Appendix B, p. 164. (It should be noticed a misprint in the third line of their Eq. (B.1) which must end in xn-1)Ramos, J.G., Vasconcellos, A.R., Garcia-Colin, L.S., (1997) Braz. J. Phys., 27, p. 585Zwanzig, R., (1981) Perspectives in Statistical Physics, pp. 123-124. , H.J. Raveché (Ed.), North-Holland, AmsterdamVasconcellos, A.R., Algarte, A.C., Luzzi, R., (1996) Braz. J. Phys., 26, p. 543Vasconcellos, A.R., Luzzi, R., Garcia-Colin, L.S., (1991) Phys. Rev. A, 43, p. 6633Vasconcellos, A.R., Luzzi, R., Garcia-Colin, L.S., (1995) Physica A, 221, p. 495Luzzi, R., Vasconcellos, A.R., Esperidião, A.S., (1995) Phys. Rev. B, 52, p. 5021Vasconcellos, A.R., Luzzi, R., Jou, D., Casas-Vázquez, J., (1995) Phys. Rev. B, 52, p. 5030Lauck, L., Vasconcellos, A.R., Luzzi, R., (1992) Phys. Rev. B, 46, p. 615
Mesoscopic Hydro-thermodynamics Of Phonons In Semiconductors: Heat Transport In Iii-nitrides
No full textIt is presented a generalized hydro-thermodynamics (called mesoscopic hydro-thermodynamics MHT) of phonons in semiconductors, driven away from equilibrium by external forces, derived by the method of moments from a generalized Peierls-Boltzmann kinetic equation built in the framework of a non-equilibrium statistical ensemble formalism. The resulting MHT involves the enormous set of coupled evolution equations for the densities of the quasi-particles (phonons) and their energy together with their fluxes of all orders. The handling of them requires the introduction of a contraction of description what defines MHT's of different orders. We illustrate the matter analyzing heat transport by phonons in GaN within the framework of a MHT of first order to obtain a generalized Guyer-Krumhansl equation from which it is analyzed the effect of geometry on the heat transport. It is described the influence of size (from bulk to nanometric scales) on the reduction of the thermal conductivity and the improving of the figure of merit of thermoelectric devices. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.865Castelvecchi, D., Collins, G.P., Fischetti, M., Mirsky, S., Moyer, M., Musser, G., Soares, C., Wong, K., (2010) Scientific American, 302, p. 68Cahill, D.G., Ford, W.K., Goodson, K.E., Mahan, G.D., Majumdar, A., Maris, H.J., Merlin, R., Phillpot, S.R., (2003) J. Appl. Phys, 93, p. 793Meijer, G.I., (1991) Science, 328, p. 318Zhang, Z.M., (2007) Nano/Microscale Heat Transfer, , McGraw Hill, New YorkTzou, D.Y., (1997) Macro to Micro Scale Heat Transport, , Taylor and Francis, WashingtonLi, N., Ren, J., Wang, L., Zhang, G., Ḧanggi, P., Li, B., (2012) Rev. Mod. Phys, 84, p. 1045Liu, S., Xu, X.F., Xie, R.G., Zhang, G., Li, B.W., (2012) Eur. Phys. J B, 85, p. 337Chowdhury, I., Prasher, R., Lofgreen, K., Chrysler, G., Narasimhan, S., Mahajan, R., Koester, D., Venkatasubramanian, R., (2009) Nature Nanotechnol, 4, p. 235Dames, C., Chen, G., (2006) Thermoelectrics Handbook: Macro to Nano, , edited by D.M. Rowe CRC Taylor and Francis, Boca RatonKlein, R., (1985) Introduction to Phonon Hydrodynamic In: Nonequilibrium Phonon Dynamics, 124. , edited by W.E. Bron Plenum, New YorkLuzzi, R., Vasconcellos, A.R., Ramos, J.G., (2002) Predictive Statistical Mechanics: A Non-Equilibrium Ensemble Formalism, , Kluwer Academic, DordrechtLuzzi, R., Vasconcellos, A.R., Ramos, J.G., (2006) Rivista Nuovo Cimento, 29, p. 1Luzzi, R., Vasconcellos, A.R., Ramos, J.G., (2000) Statistical Foundations of Irreversible Thermodynamics, , Teubner-Bertelsmann-Springer DordrechtLuzzi, R., Vasconcellos, A.R., Ramos, J.G., (2001) Rivista Nuovo Cimento, 24, p. 1Zubarev, D.N., Morozov, V., R̈opke, G., (1997) Statistical Mechanics of Non Equilibrium Processes: Relaxation and Hydrodynamic Processes, 2. , Academie Verlag-Wiley VCH, BerlinVasconcellos, A.R., Castro, A.R.B., Silva, C.A.B., Luzzi, R., J. Appl. Phys, , arXiv:1211.0342 andLauck, L., Vasconcellos, A.R., Luzzi, R., (1990) Physica A, 168, p. 789Vannucchi, F.S., Vasconcellos, A.R., Luzzi, R., (2009) Int. J. Mod. Phys B, 23, p. 5283Zubarev, D.N., Morozov, V., R̈opke, G., (1996) Statistical Mechanics of Non Equilibrium Processes: Basic Concepts, Kinetic Theory, 1. , Academie Verlag-Wiley VCH, BerlinCoveney, P., Highfield, R., (1990) The Arrow of Time, , Fawcett-Columbine, New YorkDeuderwaerdere, T., Casas Vazquez, J., Jou, D., Lebon, G., (1996) Phys. Rev E, 53, p. 498Silva, C.A.B., Ramos, J.G., Vasconcellos, A.R., Luzzi, R., (2012) Phys. Rev. eJou, D., Casas Vazquez, J., Madureira, J.R., Vasconcellos, A.R., Luzzi, R., (2001) J. Chem. Phys, 116, p. 1571Jou, D., Casas Vazquez, J., Madureira, J.R., Vasconcellos, A.R., Luzzi, R., (2001) J. Mod. Phys B, 15, p. 4211Alvarez, F.X., Jou, D., Sellito, A., (2009) J. Appl. Phys, 105, p. 014317Fano, U., (1957) Rev. Mod. Phys, 29, p. 74Bogoliubov, N.N., (1967) Lectures in Quantum Statistics i, , Gordon and Breach, New YorkKlauder, J.R., Skagerstam, B.S., (1984) Coherent States World Scientific, , SingaporePines, D., (1961) The Many-Body Problem, , Benjamin, New YorkMadureira, J.R., Vasconcellos, A.R., Luzzi, R., Lauck, L., (1998) Phys. Rev E, 57, p. 3637Ramos, J.G., Vasconcellos, A.R., Luzzi, R., (2000) J. Chem. Phys, 112, p. 2692Maxwell, J.C., (1867) Philos. Trans. Roy. Soc. Lond, 157, p. 49Heims, S.P., Jaynes, E.T., (1962) Rev. Mod. Phys, 34, p. 143. , see Appendix B in p. 164Guyer, R.A., Krumhansl, J.A., (1966) Phys. Rev, 148, p. 766Guyer, R.A., Krumhansl, J.A., (1966) Phys. Rev, 148, p. 778Ziman, J.M., (1960) Electrons and Phonons, , Clarendon OxfordFamily, F., Viazek, T., (1991) Dynamical of Fractal Surfaces, , World Scientific, SingaporeGuthy, C., Nam, C.-Y., Fischer, J.E., (2008) J. Appl. Phys, 103, p. 064319Burnett, D., (1935) Proc. Lond. Math. Soc, 40, p. 382Rodrigues, C.G., Silva, A.A.P., Silva, C.A.B., Vasconcellos, A.R., Ramos, J.G., Luzzi, R., (2010) Braz. J. Phys, 40, p. 63Luzzi, R., Vasconcellos, A.R., Casas-Vazquez, J., Jou, D., (1997) J. Chem. Phys, 107, p. 7383Luzzi, R., Vasconcellos, A.R., Casas-Vazquez, J., Jou, D., (1998) Physica A, 248, p. 111Algarte, A.C., Vasconcellos, A.R., Luzzi, R., (1992) Phys. Stat. Sol. B, 173, p. 487Algarte, A.C., Vasconcellos, A.R., Luzzi, R., (1996) Phys. Rev B, 54, p. 11311Casas-Vazquez, J., Jou, D., (2003) Rep. Prog. Phys, 66, p. 193
Considerations Of Fröhlich's Bose-einstein-like Condensation
No full textThe so-called Fröhlich effect - consisting of a conjectured coherent behavior of boson-like excitations in biological and molecular polymers - is fully derived and analyzed in terms of a thermo-mechanical theory. This is the so-called informational statistical thermodynamics, based on a generalization of Gibbs statistical theory to systems far from equilibrium. Moreover, it is shown that when double (or multiple) processes of excitation of the boson system are possible there follows a positive-feedback phenomenon that greatly favors and enhances the effect. © 1998 Elsevier Science B.V.2382-3206211Eichwald, C.F., (1995) Phys. Lett. A, 207, p. 194Fröhlich, H., (1969) From Theoretical Physics to Biology, pp. 13-22. , M. Marois (Ed.), North-Holland, AmsterdamFröhlich, H., (1968) Int. J. Quantum Chem., 2, p. 641Fröhlich, H., (1970) Nature, 228, p. 1093Fröhlich, H., (1980) Adv. Electron. Electron Phys., 17, p. 85Mesquíta, M.V., Vasconcellos, A.R., Luzzi, R., (1993) Phys. Rev. E, 48, p. 4049Zubarev, D.N., (1971) Neravnovesnaia Statisticheskaia Termodinamika Nauka, Moscow(1974) Nonequilibrium Statistical Thermodynamics, , Consultants Bureau, New YorkZubarev, D.N., Morozov, V.N., Röpke, G., (1996) Statistical Mechanics of Nonequilibrium Processes, 1. , Basic Concepts, Kinetic Theory Akademie Verlag, BerlinLuzzi, R., Vasconcellos, A.R., (1990) Fortschr. Phys., 38, p. 887Ramos, J.G., Vasconcellos, A.R., Luzzi, R., (1995) Fortschr. Phys., 43, p. 265Jaynes, E.T., Macroscopic prediction (1985) Complex Systems: Operational Approaches, , H. Haken (Ed.), Springer, BerlinJaynes, E.T., (1986) Frontiers of Nonequilibrium Statistical Physics, pp. 33-55. , G.T. Moore, M.O. Scully (Eds.), Plenum, New YorkAkhiezer, A.I., Peletminskii, S.V., (1981) Methods of Statistical Physics, , Pergamon, OxfordLauck, L., Vasconcellos, A.R., Luzzi, R., (1990) Physica A, 168, p. 789Hobson, A., (1966) J. Chem. Phys., 45, p. 1352Garcia-Colin, L.S., Vasconcellos, A.R., Luzzi, R., (1994) J. Nonequilib. Thermodyn., 19, p. 24Tenan, M.A., Vasconcellos, A.R., Luzzi, R., (1996) Fortschr. Phys., 47, p. 1Davydov, A.S., (1982) Biology and Quantum Mechanics, , Pergamon, OxfordScott, A.C., (1982) Phys. Rev. A, 26, p. 578Zubarev, D.N., Modern methods of the statistical theory of nonequilibrium processes (1980) Reviews of Science and Technology: Modern Problems of Mathematics, 16. , R.B. Gamkreludze (Ed.), Nauka, Moscow(1981) Sov. Math., 16, p. 1509(1991) R.E. Mills, Phys. Rev. A, 43, p. 3176Tuszyński, J.A., Paul, R., (1991) Phys. Rev. A, 43, p. 3179Bolterauer, H., Ludwig, L.A., (1993) Phys. Rev. E, 47, p. 2122Madureira, A.J., Vasconcellos, A.R., Luzzi, R., Lauck, L., (1996) IFGW-Unicamp Internal Report, , future publicationScott, A.C., (1992) Phys. Rep., 217, p.
On A Generalized Gibbs-boltzmann Ensemble Formalism For Dissipative Systems
No full textThe Nonequilibrium Statistical Operator Method, constructed on the basis of a generalized Gibbs-Boltzmann ensemble formalism, is gaining prominence as an approach to problems in statistical mechanics of nonequilibrium and nonlinear (dissipative) systems. In this paper, we consider the case of a generalized nonequilibrium grand-canonical ensemble. Besides the traditional densities of energy and particle number, this construction requires the introduction of the associated nonconserving dissipative fluxes of all orders. © 1998 Elsevier Science B.V. All rights reserved.2571-4424428Zubarev, D.N., Morosov, V.N., Röpke, G., (1996) Statistical Mechanics of Nonequilibrium Phenomena, Vol. 1: Basic Concepts, Kinetic Theory(1997) Relaxation and Hydrodynamic Processes, 2. , Akademie Verlag, Berlin, respectivelyLuzzi, R., Vasconcellos, A.R., (1990) Fortschr. Phys./Prog. Phys., 38, p. 887Madureira, J.R., Vasconcellos, A.R., Luzzi, R., A nonequilibrium statistical grand-canonical ensemble: Description in terms of flux operators, IFGW-unicamp internal report (1997) J. Chem. Phys., , in pressPeletminskii, S.V., Sokolovskii, A.I., (1974) Math. Theor. Phys. (USSR), 18, p. 121Luzzi, R., Vasconcellos, A.R., (1997) Physica A, 241, p. 667Ramos, J.G., Vasconcellos, A.R., Garcia-Colin, L.S., (1997) Braz. J. Phys., 27, p. 58
A Nonequilibrium Statistical Ensemble Formalism: Maxent-nesom: Basic Concepts, Construction, Application, Open Questions And Criticisms
No full textWe describe a particular approach for the construction of a nonequilibrium statistical ensemble formalism for the treatment of dissipative many-body systems. This is the so-called Nonequilibrium Statistical Operator Method, based on the seminal and fundamental ideas set forward by Boltzmann and Gibbs. The existing approaches can be unified under a unique variational principle, namely, MaxEnt, which we consider here. The main six basic steps that are at the foundations of the formalism are presented and the fundamental concepts are discussed. The associated nonlinear quantum kinetic theory and the accompanying Statistical Thermodynamics (the Informational Statistical Thermodynamics) are very briefly described. The corresponding response function theory for systems away from equilibrium allows to connected the theory with experiments, and some examples are summarized; there follows a good agreement between theory and experimental data in the cases in which the latter are presently available. We also present an overview of some conceptual questions and associated criticisms.142831893264Oreskes, N., Shrader-Frechette, K., Beltz, K., (1994) Science, 263, p. 641Penrose, O., (1979) Rep. Prog. Phys., 42, p. 1938Kubo, R., (1978) Prog. Theo. Phys., 64 (SUPPL.), p. 1Jaynes, E.T., (1986), pp. 33-55. , Frontiers of Nonequilibrium Statistical Physics, eds. G. T. Moore and M. O. Scully (Plenum, New York)Zwanzig, R., (1965), pp. 67-102. , Annual Review of Physical Chemistry Vol. 16 (Academic Press, New York)(1981), pp. 123-124. , Perspectives in Statistical Physics, ed. H. J. Raveché (North Holland, Amsterdam)Kirkwood, J.G., (1946) J. Chem. Phys., 14, p. 180Green, M.S., (1952) J. Chem. 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Positive-feedback-enhanced Fröhlich's Bose-einstein-like Condensation In Biosystems
No full textWe present a mechanostatistical study of the so-called Fröhlich effect, namely nonthermal amplification of polar vibrations leading to complex behavior in biosystems, like biopolymers and large aggregates of macromolecules. Fröhlich condensation is considered to be of relevance for a certain class of biological processes, in particular in connection with the problem of long-range propagation of signals at physiological temperature. Resorting to a thermomechanical theory appropriate to deal with irreversible processes in systems far from equilibrium, earlier results are extended. We perform an analysis of the case when production of a double excitation of polar vibrations, generated by the action of an external pumping source of metabolic energy, is possible. It is shown that, when this is the case, the process involves a positive feedback mechanism that greatly facilitates and enhances the phenomenon of Fröhlich's condensation, and consequently the possible accompanying biological processes. The results are discussed and eventual connection with experimental observations pointed out. © 1998 John Wiley & Sons, Inc.662177187Zubarev, D.N., (1974) Nonequilibrium Statistical Thermodynamics, , Consultants Bureau, New YorkNeravnovesnaia, (1971) Statisticheskaia Termodinamika, , ldz. Nauka, MoscowZubarev, D.N., (1980) Reviews of Science and Technology: Modern Problems of Mathematics, 16. , R. B. Gamkreludze, Ed. Izd. Nauka, Moscow(1981) Soviet Math., 16, p. 1509Zubarev, D.N., Morozov, V.N., Röpke, G., (1996) Statistical Mechanics of Nonequilibrium Processes, , Akademie, BerlinJaynes, E.T., (1986) Frontiers of Nonequilibrium Statstical Physics, pp. 33-55. , G. T. Moore and M. O. Scully, Eds. Plenum, New YorkJaynes, E.T., (1985) Complex Systems: Operational Approaches, , H. Haken, Ed. Springer, BerlinAkhiezer, A.I., Peletminskii, S.V., (1981) Methods of Statistical Physics, , Pergamon, OxfordLauck, L., Vasconcellos, A.R., Luzzi, R., (1990) Physica A, 168, p. 789Garcia-Colin, L.S., Vasconcellos, A.R., Luzzi, R., (1994) J. Non-Equilib. Thermodyn., 19, p. 24Fröhlich, H., (1969) From Theoretical Physics to Biology, pp. 13-22. , M. Marois, Ed. North Holland, AmsterdamFröhlich, H., (1980) Advances in Electronics and Electron Physics, 17, pp. 85-152. , Academic, New YorkAnderson, P.W., (1972) Science, 117, p. 393Nicolis, G., Prigogine, I., (1989) Exploring Complexity, , Freeman, New YorkMesquita, M.V., Vasconcellos, A.R., Luzzi, R., (1993) Phys. Rev. E, 48, p. 4049Mascarenhas, S., (1987) Electrets, pp. 321-346. , G. M. Sessler, Ed. Springer, BerlinBlitz, H., Bütner, R., Fröhlich, H., (1981) Z. Naturforsch. B, 36, p. 206Fröhlich, H., (1970) Nature, 228, p. 1093Mills, R.E., (1983) Phys. Rev. A, 28, p. 379Paul, R., Fritz, O.G., Chattetjee, R., (1988) Int. J. Quant. Chem. Symp., 15, p. 191Davydov, A.S., (1982) Biology and Quantum Mechanics, , Pergamon, OxfordScott, A.C., (1982) Phys. Rev. A, 26, p. 578Davydov, A.S., (1986) Solitons, pp. 1-51. , S. E. Trullinger, V. E. Zakharov, and V. L. Prokovsky, Eds. Elsevier, New York, Chap. 1Scott, A.C., (1992) Phys. Rep, 217, p. 1Luzzi, R., Vasconcellos, A.R., (1993) Phys. Rev. E, 48, p. 2246Prigogine, I., (1969) From Theoretical Physics to Biology, , M. Marois, Ed. North Holland, AmsterdamWebb, S.J., Stoneham, M.E., Fröhlich, H., (1977) Phys. Lett. A, 63, p. 407Drissler, F., MacFarlane, R.M., (1978) Phys. Lett. A, 69, p. 65Wu, T.M., Austin, S., (1978) J. Theor. Biol., 71, p. 209Fröhlich, H., (1981) Collective Phenomena, 3, p. 139Rowlands, S., Sewchand, L.S., Lovlin, R.E., Beck, J.S., Enns, E.G., (1981) Phys. Lett. A, 82 A, p. 436Rowlands, S., Sewchand, L.S., Enns, E.G., (1982) Phys. Lett. A, 87, p. 256Tuszynski, J.A., (1988) J. Theor. Biol., 132, p. 31Careri, G., Buotempo, U., Carta, R., Gratton, E., Scott, A.C., (1983) Phys. Rev. Lett., 51, p. 304Lauck, L., Vasconcellos, A.R., Luzzi, R., (1992) Phys. Rev. B, 46, p. 6150Mills, R.E., (1991) Phys. Rev. A, 43, p. 3176Tuszyński, J.A., Paul, R., (1991) Phys. Rev. A, 43, p. 3179Bolterauer, H., Ludwig, L.A., (1993) Phys. Rev. E, 47, p. 2122Mesquita, M.V., Vasconcellos, A.R., Luzzi, R., Phys. Lett. A, , submitte
Non-equilibrium Statistical Mechanics Of Complex Systems: An Overview
No full textThe ensemble formalism has been extremely successful in the handling of the grandiose theoretical scheme of statistical mechanics and thermodynamics initiated by Maxwell, Boltzmann and Gibbs, which has been given concrete and consistent foundations to the study of the many situations present in condensed-matter physics. However, its use is hampered when dealing with certain complex phenomena for which the researcher may not have an access to the information on all the constraints relevant to the problem in hands (so-called hidden constraints), which leads to poor predictions. In an attempt to improve predictions there have been introduced, beginning in the past 1950s, and pioneered by P. Lèvy in the 1930s, auxiliary approaches which attempt to assuage the difficulty, but at the price of not being fully consistent and depending on free parameters. This is done in the framework of the variational (extremum principle) approach in statistical mechanics founded on information theory. In it, the general and well-established Boltzmann-Gibbs canonical scheme follows from maximization with given constraints of Gibbs-Boltzmann-Shannon information-theoretic entropy (better called measure of uncertainty of information) : it is considered to be the only consistent probability measure of information. The other (say non-canonical or heterotypical) auxiliary approaches are based on replacing GBS information-theoretic entropy by others, which are used to derive non-conventional probability distributions for non-equilibrium systems. We present a detailed description of their construction and a clarification of their scope, interpretation and utility. Also, resorting to the particular case of Renyi's approach the construction of a non-equilibrium ensemble formalism is described. The non-conventional distribution functions of fermions and bosons are discussed. The use of the formalism is illustrated via the analysis of experimental results in the case of fractal-like structured systems. Also a purely theoretical analysis is done in the cases of an ideal gas and of radiation comparing the conventional and non-conventional approaches. In all of these situations it is discussed which are the difficulties involved (hidden constraints in an insufficient description) which require to resort to the non-conventional approach, and what determines the value of the parameter(s) that the formalism introduces in each case, namely, its (their) dependence on the system characteristics and the experimental protocol. © Società Italiana di Fisica.30395157MONTROLL, E.W., SHLESINGER, M.F., (1983) J. Stat. Phys, 12, p. 209FISHER, R.A., (1922) Philos. Trans. R. Soc. London A, 222, p. 309BALIAN, R., (1999) Am. J. Phys, 67, p. 1078LANDSBERG, P.T., (1999) Braz. J. 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