Analytic results for the Tsallis thermodynamic variables

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dc.contributor.authorBhattacharyya, Trambak
dc.contributor.authorCleymans, Jean
dc.contributor.authorMogliacci, Sylvain
dc.date.accessioned2021-10-08T07:11:33Z
dc.date.available2021-10-08T07:11:33Z
dc.date.issued2016
dc.description.abstractWe analytically investigate the thermodynamic variables of a hot and dense system, in the framework of the Tsallis non-extensive classical statistics. After a brief review, we start by recalling the corresponding massless limits for all the thermodynamic variables. We then present the detail of calculation for the exact massive result regarding the pressure -- valid for all values of the $q$-parameter -- as well as the Tsallis $T$-, $mu$- and $m$- parameters, the former characterizing the non-extensivity of the system. The results for other thermodynamic variables, in the massive case, readily follow from appropriate differentiations of the pressure, for which we provide the necessary formulas. For the convenience of the reader, we tabulate all of our results. A special emphasis is put on the method used in order to perform these computations, which happens to reduce cumbersome momentum integrals into simpler ones. Numerical consistency between our analytic results and the corresponding usual numerical integrals are found to be perfectly consistent. Finally, it should be noted that our findings substantially simplify calculations within the Tsallis framework. The latter being extensively used in various different fields of science as for example, but not limited to, high-energy nucleus collisions, we hope to enlighten a number of possible applications. Bhattacharyya, Trambak; Cleymans, Jean; Mogliacci, Sylvain
dc.identifier.apacitationBhattacharyya, T., Cleymans, J., & Mogliacci, S. (2016). Analytic results for the Tsallis thermodynamic variables. <i>Physical Review D - Particles, Fields, Gravitation, and Cosmology</i>, 94(9), 174 - 177. http://hdl.handle.net/11427/34640en_ZA
dc.identifier.chicagocitationBhattacharyya, Trambak, Jean Cleymans, and Sylvain Mogliacci "Analytic results for the Tsallis thermodynamic variables." <i>Physical Review D - Particles, Fields, Gravitation, and Cosmology</i> 94, 9. (2016): 174 - 177. http://hdl.handle.net/11427/34640en_ZA
dc.identifier.citationBhattacharyya, T., Cleymans, J. & Mogliacci, S. 2016. Analytic results for the Tsallis thermodynamic variables. <i>Physical Review D - Particles, Fields, Gravitation, and Cosmology.</i> 94(9):174 - 177. http://hdl.handle.net/11427/34640en_ZA
dc.identifier.issn1550-2368
dc.identifier.issn1550-7998
dc.identifier.ris TY - Journal Article AU - Bhattacharyya, Trambak AU - Cleymans, Jean AU - Mogliacci, Sylvain AB - We analytically investigate the thermodynamic variables of a hot and dense system, in the framework of the Tsallis non-extensive classical statistics. After a brief review, we start by recalling the corresponding massless limits for all the thermodynamic variables. We then present the detail of calculation for the exact massive result regarding the pressure -- valid for all values of the $q$-parameter -- as well as the Tsallis $T$-, $mu$- and $m$- parameters, the former characterizing the non-extensivity of the system. The results for other thermodynamic variables, in the massive case, readily follow from appropriate differentiations of the pressure, for which we provide the necessary formulas. For the convenience of the reader, we tabulate all of our results. A special emphasis is put on the method used in order to perform these computations, which happens to reduce cumbersome momentum integrals into simpler ones. Numerical consistency between our analytic results and the corresponding usual numerical integrals are found to be perfectly consistent. Finally, it should be noted that our findings substantially simplify calculations within the Tsallis framework. The latter being extensively used in various different fields of science as for example, but not limited to, high-energy nucleus collisions, we hope to enlighten a number of possible applications. Bhattacharyya, Trambak; Cleymans, Jean; Mogliacci, Sylvain DA - 2016 DB - OpenUCT DP - University of Cape Town IS - 9 J1 - Physical Review D - Particles, Fields, Gravitation, and Cosmology LK - https://open.uct.ac.za PY - 2016 SM - 1550-2368 SM - 1550-7998 T1 - Analytic results for the Tsallis thermodynamic variables TI - Analytic results for the Tsallis thermodynamic variables UR - http://hdl.handle.net/11427/34640 ER - en_ZA
dc.identifier.urihttp://hdl.handle.net/11427/34640
dc.identifier.vancouvercitationBhattacharyya T, Cleymans J, Mogliacci S. Analytic results for the Tsallis thermodynamic variables. Physical Review D - Particles, Fields, Gravitation, and Cosmology. 2016;94(9):174 - 177. http://hdl.handle.net/11427/34640.en_ZA
dc.language.isoeng
dc.publisher.departmentAccounting and Accountability in Africa
dc.publisher.facultyFaculty of Commerce
dc.sourcePhysical Review D - Particles, Fields, Gravitation, and Cosmology
dc.source.journalissue9
dc.source.journalvolume94
dc.source.pagination174 - 177
dc.source.urihttps://dx.doi.org/10.1103/PhysRevD.94.094026
dc.subject.otherCondensed Matter - Statistical Mechanics
dc.subject.otherHigh Energy Physics - Phenomenology
dc.titleAnalytic results for the Tsallis thermodynamic variables
dc.typeJournal Article
uct.type.publicationResearch
uct.type.resourceJournal Article
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