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2004 | 2 | 2 | 241-253
Tytuł artykułu

Thermodynamic non-additivity in disordered systems with extended phase space

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.
Wydawca

Czasopismo
Rocznik
Tom
2
Numer
2
Strony
241-253
Opis fizyczny
Daty
wydano
2004-06-01
online
2004-06-01
Twórcy
  • Laboratoire de Electrochimie et Chimie Analytique, Ecole Nationale Superieure de Chimie de Paris-Universite Pierre et Marie Curie, 11 rue P. et M. Curie, 75231 Cedex 05, Paris, France, vakarin@ccr.jussieu.fr
autor
  • Laboratoire de Electrochimie et Chimie Analytique, Ecole Nationale Superieure de Chimie de Paris-Universite Pierre et Marie Curie, 11 rue P. et M. Curie, 75231 Cedex 05, Paris, France
Bibliografia
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  • [2] A periodically updated bibliography can be found at http://152.84.252.115/TEMUCO.pdf.
  • [3] C. Tsallis and D.J. Bukman: “Anomalous diffusion in the presence of external forces: Exact time-dependent solutions and their thermostatistical basis”, Phys. Rev. E, Vol. 54, (1996), R2197-R2200. http://dx.doi.org/10.1103/PhysRevE.54.R2197[Crossref]
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  • [5] H. Touchette: “When is a quantity additive, and when is it extensive?”, Physica A, Vol. 305, (2002), pp. 84–88. http://dx.doi.org/10.1016/S0378-4371(01)00644-6[Crossref]
  • [6] E.M.F. Curado and C. Tsallis: “Generalized statistical mechanics: Connection with thermodynamics”, J. Phys. A, Vol. 24, (1991), pp. L69–L72. http://dx.doi.org/10.1088/0305-4470/24/2/004[Crossref]
  • [7] C. Tsallis, R.S. Mendes, and A.R. Plastino: “The role of constraints within generalized nonextensive statistics”, Physica A, Vol. 261, (1998), pp. 534–554. http://dx.doi.org/10.1016/S0378-4371(98)00437-3[Crossref]
  • [8] A. Renyi: Probability theory, North Holland, Amsterdam, 1970.
  • [9] R.J.V. dos Santos: “Generalization of Shannon’s theorem for Tsallis entropy”, J. Math. Phys., Vol. 38, (1997), pp. 4104–4107. http://dx.doi.org/10.1063/1.532107[Crossref]
  • [10] S. Abe: “Axioms and uniqueness theorem for Tsallis entropy”, Phys. Lett. A, Vol. 271, (2000), pp. 74–79. http://dx.doi.org/10.1016/S0375-9601(00)00337-6[Crossref]
  • [11] P.A. Alemany, “Possible connection of the generalized thermostatistics with a scale invariant statistical thermodynamics”, Phys. Lett. A, Vol. 235, (1997), pp. 452–456. http://dx.doi.org/10.1016/S0375-9601(97)00689-0[Crossref]
  • [12] C. Beck: “Non-additivity of Tsallis entropies and fluctuations of temperature”, Europhys. Lett., Vol. 57, (2002), pp. 329–333. http://dx.doi.org/10.1209/epl/i2002-00464-8[Crossref]
  • [13] G. Wilk, and Z. Wlodarczyk: “Interpretation of the Nonextensive parameter q in Some Applications of Tsallis Statistics and Levy Distributions”, Phys. Rev. Lett., Vol. 84, (2000), pp. 2770–2773. http://dx.doi.org/10.1103/PhysRevLett.84.2770[Crossref]
  • [14] M.P. Almeida: “Generalized entropies from first principles”, Physica A, Vol. 300, (2001), pp. 424–432. http://dx.doi.org/10.1016/S0378-4371(01)00353-3[Crossref]
  • [15] E.G.D. Cohen: “Statistics and dynamics”, Physica A, Vol. 305, (2003), pp. 19–26. http://dx.doi.org/10.1016/S0378-4371(01)00634-3[Crossref]
  • [16] M. Nauenberg: “Critique of q-entropy for thermal statistics”, Phys. Rev. E Vol. 67, (2003), pp. 036114-1–036114-6. http://dx.doi.org/10.1103/PhysRevE.67.036114
  • [17] C. Beck and E.G.D. Cohen: “Superstatistics”, Physica A, Vol. 322, (2003), pp. 267–275. http://dx.doi.org/10.1016/S0378-4371(03)00019-0[Crossref]
  • [18] C. Tsallis: “Non-extensive thermostatistics: Brief review and comments”, Physica A, Vol. 221, (1995), pp. 277–290. http://dx.doi.org/10.1016/0378-4371(95)00236-Z[Crossref]
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  • [20] D. Sherrington and S. Kirkpatrick: “Solvable model of a Spin Glass”, Phys. Rev. Lett., Vol. 35, (1975), pp. 1792–1796. http://dx.doi.org/10.1103/PhysRevLett.35.1792[Crossref]
  • [21] G. Parisi: “Physics of glassy systems”, Nucl. Phys. B (Proc. Suppl.), Vol. 83–84, (2000), pp. 82–92.
  • [22] E.V. Vakarin and J.P. Badiali: “Role of structural fluctuations in the insertion into complex host matrices”, arXiv: cond-mat/0312153, 2003.
  • [23] M. Mezard, G. Parisi, and M. Virasoro: Spin Glass Theory and Beyond, World Scientific, Singapore, 1987.
  • [24] Here we do not discuss the problems of the replica theory itself, such as the limiting procedure or the replica symmetry breaking.
  • [25] J.S. Andrade Jr., M.P. Almeida, A.A. Moreira, and G.A. Farias: “Extended phase-space dynamics for the generalized non-extensive thermostatistics”, Phys. Rev. E, Vol. 65, (2002), pp. 036121-1–036121-5. http://dx.doi.org/10.1103/PhysRevE.65.036121
  • [26] D. Sherrington: “Ising replica magnets”, J. Phys. A, Vol. 13, (1980), pp. 637–649. http://dx.doi.org/10.1088/0305-4470/13/2/027[Crossref]
  • [27] R.W. Penney, A.C.C. Coolen, and D. Sherrington: “Coupled dynamics of fast spins and slow interactions in neural networks and spin systems”, J. Phys. A, Vol. 26, (1993), pp. 3681–3695. http://dx.doi.org/10.1088/0305-4470/26/15/018[Crossref]
  • [28] V. Dotsenko, S. Franz, and M. Mezard: “Partial annealing and overfrustration in disordered systems”, J. Phys. A, Vol. 27, (1994), pp. 2351–2365. http://dx.doi.org/10.1088/0305-4470/27/7/016[Crossref]
  • [29] D.E. Feldman and V.S. Dotsenko: “Partially annealed neural networks”, J. Phys. A, Vol. 27, (1994), pp. 4401–4411. http://dx.doi.org/10.1088/0305-4470/27/13/015[Crossref]
  • [30] B. Derrida: “From random walks to spin glasses”, Physica D, Vol. 107, (1997), pp. 186–198. http://dx.doi.org/10.1016/S0167-2789(97)00086-9[Crossref]
  • [31] G. Ruppeiner: “Riemannian geometry in the thermodynamic fluctuation theory”, Rev. Mod. Phys., Vol. 67, (1995), pp. 605–659. http://dx.doi.org/10.1103/RevModPhys.67.605[Crossref]
  • [32] E. Vives and A. Planes: “Is Tsallis Thermodynamics Nonextensive?”, Phys. Rev. Lett., Vol. 88, (2002), pp. 020601-1–020601-4.
  • [33] Q.A. Wang: “Incomplete statistics: Nonextensive generalizations of statistical mechanics”, Chaos, Solitons and Fractals, Vol. 12, (2001), pp. 1431–1437. http://dx.doi.org/10.1016/S0960-0779(00)00113-2[Crossref]
  • [34] Q.A. Wang: “Nonextensive statistics and incomplete information”, Eur. Phys. J. B, Vol. 26, (2002), pp. 357–368. http://dx.doi.org/10.1007/s10051-002-8974-4[Crossref]
  • [35] E.V. Vakarin, J.P. Badiali, M.D. Levi, and D. Aurbach: “Role of host distortion in the intercalation process”, Phys. Rev. B, Vol. 63, (2001), pp. 014304-1–014304-6.
  • [36] E.V. Vakarin and J.P. Badiali: “Interplay of Configurational and Structural Transitions in the Course of Intercalation”, J. Phys. Chem. B, Vol. 106, (2002), pp. 7721–7724. http://dx.doi.org/10.1021/jp0209190[Crossref]
  • [37] E.V. Vakarin, A.E. Filippov, and J.P. Badiali: “Distortion of a Substrate Induced by Adsorption at Solid-Liquid Interfaces”, Phys. Rev. Lett., Vol. 81, (1998), pp. 3904–3907. http://dx.doi.org/10.1103/PhysRevLett.81.3904[Crossref]
  • [38] E.V. Vakarin and J.P. Badiali: “Roughening transition in the presence of adsorbates”, Phys. Rev. B, Vol. 60, (1999), pp. 2064–2067. http://dx.doi.org/10.1103/PhysRevB.60.2064[Crossref]
  • [39] A.B. Adib, A.A. Moreira, J.S. Andrade Jr., and M. P. Almeida: “Tsallis thermostatistics for finite systems: A Hamiltonian approach”, Physica A Vol. 322, (2003), pp. 276–284. http://dx.doi.org/10.1016/S0378-4371(02)01601-1[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02475630
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