General Deformations

  • Jan Naudts


The notion of deformed exponential and logarithmic functions is further generalised. This leads to a rather general definition of a deformed exponential family. The site percolation problem is discussed as an example.


Logarithmic Function Exponential Family Cauchy Distribution Deduce Logarithm General Deformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Charalambides, C.A., Papadatos, N.: The q-factorial moments of discrete q-distributions and a characterization of the Euler distribution. In:   N. Balakrishnan, I.G. Bairamov, O.L. Gebizlioglu (eds.) Advances on Models, Characterizations and Applications, pp. 57–71. Chapman & Hall/CRC Press, Boca Raton (2005) CrossRefGoogle Scholar
  2. 2.
    Kaniadakis, G.: Non-linear kinetics underlying generalized statistics. Physica A 296, 405–425 (2001) MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kaniadakis, G., Scarfone, A.: A new one parameter deformation of the exponential function. Physica A 305, 69–75 (2002) MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Naudts, J.: Deformed exponentials and logarithms in generalized thermostatistics. Physica A 316, 323–334 (2002) MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Naudts, J.: Estimators, escort probabilities, and phi-exponential families in statistical physics. J. Ineq. Pure Appl. Math. 5, 102 (2004) MathSciNetGoogle Scholar
  6. 6.
    Naudts, J.: Generalized thermostatistics and mean field theory. Physica A 332, 279–300 (2004) CrossRefMathSciNetGoogle Scholar
  7. 7.
    Naudts, J.: Generalized thermostatistics based on deformed exponential and logarithmic functions. Physica A 340, 32–40 (2004) CrossRefMathSciNetGoogle Scholar
  8. 8.
    Naudts, J.: Escort operators and generalized quantum information measures. Open Systems and Information Dynamics 12, 13–22 (2005) MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Naudts, J.: Parameter estimation in nonextensive thermostatistics. Physica A 365, 42–49 (2006) CrossRefGoogle Scholar
  10. 10.
    Naudts, J.: Continuity of a class of entropies and relative entropies. Rev. Math. Phys. 16, 809822 (2004); Errata. Rev. Math. Phys. 21, 947–948 (2009) CrossRefMathSciNetGoogle Scholar
  11. 11.
    Stauffer, D.: Introduction to percolation theory. Plenum Press, New York (1985) MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of AntwerpAntwerpBelgium

Personalised recommendations