Full-text resources of PSJD and other databases are now available in the new Library of Science.
Visit https://bibliotekanauki.pl


Preferences help
enabled [disable] Abstract
Number of results


2004 | 2 | 2 | 241-253

Article title

Thermodynamic non-additivity in disordered systems with extended phase space


Title variants

Languages of publication



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.










Physical description


1 - 6 - 2004
1 - 6 - 2004


  • 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
  • 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


  • [1] C.A. Tsallis: “Possible Generalization of Boltzmann-Gibbs Statistics”, J. Stat. Phys., Vol. 52, (1988), pp. 479–487. http://dx.doi.org/10.1007/BF01016429[Crossref]
  • [2] A periodically updated bibliography can be found at
  • [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]
  • [4] E.T. Jaynes: “Information Theory and Statistical Mechanics”, Phys. Rev., Vol. 106, (1957), pp. 620–630. http://dx.doi.org/10.1103/PhysRev.106.620[Crossref]
  • [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]
  • [19] J.A. Given: “On the thermodynamics of fluids adsorbed in porous media”, J. Chem. Phys., Vol. 102, (1995), pp. 2934–2945. http://dx.doi.org/10.1063/1.468601[Crossref]
  • [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]

Document Type

Publication order reference


YADDA identifier

JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.