IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v506y2018icp857-867.html
   My bibliography  Save this article

Radial distribution function within the framework of the Tsallis statistical mechanics

Author

Listed:
  • Bafghi, Seyed Mohammad Amin Tabatabaei
  • Kamalvand, Mohammad
  • Morsali, Ali
  • Bozorgmehr, Mohammad Reza

Abstract

This study is conducted to obtain the radial distribution function (RDF) within the Tsallis statistical mechanics. To this end, probability distribution functions are applied in the first and fourth versions of the Tsallis statistics. Moreover, a closed formula is proposed for RDF. The power nature of the probability distribution in the Tsallis statistics makes it difficult to separate kinetic energy and configurational potential parts. By using the Taylor expansion around q=1 of the power distribution, it is possible to show the independency of momenta and coordinates through integrating over the phase space variables. In addition, at low densities, numerical calculations have been performed for the RDF. Our results show that the correlation increases as q values increase.

Suggested Citation

  • Bafghi, Seyed Mohammad Amin Tabatabaei & Kamalvand, Mohammad & Morsali, Ali & Bozorgmehr, Mohammad Reza, 2018. "Radial distribution function within the framework of the Tsallis statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 857-867.
    • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:857-867
    DOI: 10.1016/j.physa.2018.04.107
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118305351
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.04.107?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Nelson, Kenric P. & Umarov, Sabir R. & Kon, Mark A., 2017. "On the average uncertainty for systems with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 30-43.
    2. Aragão-Rêgo, H.H & Soares, D.J & Lucena, L.S & da Silva, L.R & Lenzi, E.K & Sau Fa, Kwok, 2003. "Bose–Einstein and Fermi–Dirac distributions in nonextensive Tsallis statistics: an exact study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(1), pages 199-208.
    3. Tirnakli, Uǧur & Büyükkiliç, Fevzi & Demirhan, Doǧan, 1997. "Generalized distribution functions and an alternative approach to generalized Planck radiation law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 240(3), pages 657-664.
    4. de Oliveira, H.P. & Soares, I.Damião & Tonini, E.V., 2001. "Universality in the chaotic dynamics associated with saddle-centers critical points," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 348-358.
    5. Zhang, Qi & Luo, Chuanhai & Li, Meizhu & Deng, Yong & Mahadevan, Sankaran, 2015. "Tsallis information dimension of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 707-717.
    6. Guo, Ran & Du, Jiulin, 2014. "The adiabatic static linear response function in nonextensive statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 414-420.
    7. Mebrouk, Khireddine & Gougam, Leila Ait & Tribeche, Mouloud, 2016. "Nonextensive statistical mechanics approach to electron trapping in degenerate plasmas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 525-532.
    8. Barboza, Edésio M. & Nunes, Rafael da C. & Abreu, Everton M.C. & Ananias Neto, Jorge, 2015. "Dark energy models through nonextensive Tsallis’ statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 301-310.
    9. Kharchenko, Dmitrii O. & Kharchenko, Vasilii O., 2005. "Evolution of a stochastic system within the framework of Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 262-280.
    10. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
    11. Ochiai, T. & Nacher, J.C., 2009. "On the construction of complex networks with optimal Tsallis entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4887-4892.
    12. Abe, Sumiyoshi, 1999. "Correlation induced by Tsallis’ nonextensivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(2), pages 403-409.
    13. Chamati, H. & Djankova, A.Ts. & Tonchev, N.S., 2006. "On the application of nonextensive statistical mechanics to the black-body radiation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(2), pages 297-303.
    14. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    15. Martı́nez, S & Nicolás, F & Pennini, F & Plastino, A, 2000. "Tsallis’ entropy maximization procedure revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 286(3), pages 489-502.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Deeb, Omar El, 2023. "Entropic spatial auto-correlation of voter uncertainty and voter transitions in parliamentary elections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    2. Lucia, Umberto, 2010. "Maximum entropy generation and κ-exponential model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4558-4563.
    3. Deng, Xinyang & Deng, Yong, 2014. "On the axiomatic requirement of range to measure uncertainty," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 163-168.
    4. Tsallis, Constantino & Borges, Ernesto P., 2023. "Time evolution of nonadditive entropies: The logistic map," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    6. Rovenchak, Andrij & Sobko, Bohdana, 2019. "Fugacity versus chemical potential in nonadditive generalizations of the ideal Fermi-gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    7. López-Rosa, S. & Angulo, J.C. & Dehesa, J.S. & Yáñez, R.J., 2008. "Existence conditions and spreading properties of extreme entropy D-dimensional distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(10), pages 2243-2255.
    8. da Silva, Sérgio Luiz Eduardo Ferreira, 2021. "Newton’s cooling law in generalised statistical mechanics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    9. Preda, Vasile & Dedu, Silvia & Sheraz, Muhammad, 2014. "New measure selection for Hunt–Devolder semi-Markov regime switching interest rate models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 350-359.
    10. Naudts, Jan, 2004. "Generalized thermostatistics based on deformed exponential and logarithmic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 32-40.
    11. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    12. da Silva, Sérgio Luiz Eduardo Ferreira & dos Santos Lima, Gustavo Zampier & de Araújo, João Medeiros & Corso, Gilberto, 2021. "Extensive and nonextensive statistics in seismic inversion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
    13. Guha, Atanu & Das, Prasanta Kumar, 2018. "An extensive study of Bose–Einstein condensation in liquid helium using Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 272-284.
    14. Dukkipati, Ambedkar & Murty, M. Narasimha & Bhatnagar, Shalabh, 2006. "Nonextensive triangle equality and other properties of Tsallis relative-entropy minimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 124-138.
    15. Naif Alotaibi & A. S. Al-Moisheer & Ibrahim Elbatal & Mansour Shrahili & Mohammed Elgarhy & Ehab M. Almetwally, 2023. "Half Logistic Inverted Nadarajah–Haghighi Distribution under Ranked Set Sampling with Applications," Mathematics, MDPI, vol. 11(7), pages 1, April.
    16. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    17. Yuri Biondi & Simone Righi, 2019. "Inequality, mobility and the financial accumulation process: a computational economic analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 93-119, March.
    18. Duan, Shuyu & Wen, Tao & Jiang, Wen, 2019. "A new information dimension of complex network based on Rényi entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 529-542.
    19. Tapiero, Oren J., 2013. "A maximum (non-extensive) entropy approach to equity options bid–ask spread," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(14), pages 3051-3060.
    20. Igor Lazov, 2019. "A Methodology for Revenue Analysis of Parking Lots," Networks and Spatial Economics, Springer, vol. 19(1), pages 177-198, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:857-867. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.