On the problem of constraints in nonextensive formalism: A quantum mechanical treatment

Bagci, G. B.
Arda, Altug
Sever, Ramazan
Relative entropy (divergence) of Bregman type recently proposed by T. D. Frank and Jan Naudts is considered and its quantum counterpart is used to calculate purity of the Werner state in nonextensive formalism. It has been observed that two different expressions arise due to two different forms of quantum divergences. It is then argued that the difference is due to the fact that the relative entropy of Bregman type is related to the first choice thermostatistics whereas one of Csiszar type is related to the third-choice thermostatistics. The superiority of the third-choice thermostatistics to the first-choice thermostatistics has been deduced by noticing that the expression obtained by using the Bregman type leads to negative values for q is an element of (0, 1) and fidelity F smaller than I whereas the one obtained by using Csiszar type is free from such anomalies. Moreover, it has been noted that these two measures show different qualitative behavior with respect to F. Contrary to the classical case, the violation of the positive definiteness of the relative entropy immediately results in a choice between the two constraints without any need of more abstract Shore-Johnson axioms. The possibility of writing a relative entropy of Bregman type compatible with the third choice has been investigated further. The answer turns out to be negative as far as the usual transformation from ordinary probabilities to the escort probabilities are considered.


Akturk, Ethem; ÖZCAN, ÖZGÜR; Sever, Ramazan (World Scientific Pub Co Pte Lt, 2009-04-30)
Time-dependent joint entropy is obtained for harmonic oscillator with the time-dependent mass and frequency case. It is calculated by using time-dependent wave function obtained via Feynman path integral method. Variation of time dependence is investigated for various cases.
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Ay, Ahmet; GÜRSES, METİN; Zheltukhın, Kostyantyn (AIP Publishing, 2003-12-01)
The Hamiltonian formulation of N=3 systems is considered in general. The most general solution of the Jacobi equation in R-3 is proposed. The form of the solution is shown to be valid also in the neighborhood of some irregular points. Compatible Poisson structures and corresponding bi-Hamiltonian systems are also discussed. Hamiltonian structures, the classification of irregular points and the corresponding reduced first order differential equations of several examples are given. (C) 2003 American Institute...
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Guerses, Metin; Habibullin, Ismagil; Zheltukhın, Kostyantyn (AIP Publishing, 2008-10-01)
The concept of integrable boundary conditions is applied to hydrodynamic type systems. Examples of such boundary conditions for dispersionless Toda systems are obtained. The close relation of integrable boundary conditions with integrable reductions in multifield systems is observed. The problem of consistency of boundary conditions with the Hamiltonian formulation is discussed. Examples of Hamiltonian integrable hydrodynamic type systems on a segment and a semiline are presented. (C) 2008 American Institut...
Study of phase transitions in polymorphic liquid crystals
Nesrullajev, A; Salihoglu, S; Yurtseven, Hasan Hamit (World Scientific Pub Co Pte Lt, 1998-01-01)
This work presents our investigations of mezomorphic properties of two polymorphic liquid crystals, namely, 4-nonyloxy-4-butoxyphenyl benzoate and N-(-4-heptyloxybenzylidene-4-butylaniline) in a wide temperature range, particularly, in the phase transition regions. By means of an original Experimental method. the heterophase regions and also the phase transition temperatures have been determined for these materials with high accuracy. These phase transition intervals have been analyzed using a mean field mo...
Consistency problem of the solutions of the space fractional Schrodinger equation
Bayin, Selcuk S. (AIP Publishing, 2013-09-01)
Recently, consistency of the infinite square well solution of the space fractional Schrodinger equation has been the subject of some controversy. Hawkins and Schwarz [J. Math. Phys. 54, 014101 (2013)] objected to the way certain integrals are evaluated to show the consistency of the infinite square well solutions of the space fractional Schrodinger equation [S. S. Bayin, J. Math. Phys. 53, 042105 (2012); 53, 084101 (2012)]. Here, we show for general n that as far as the integral representation of the soluti...
Citation Formats
G. B. Bagci, A. Arda, and R. Sever, “On the problem of constraints in nonextensive formalism: A quantum mechanical treatment,” INTERNATIONAL JOURNAL OF MODERN PHYSICS B, pp. 2085–2092, 2006, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/62774.