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Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions

Received: 13 February 2022     Accepted: 29 March 2022     Published: 20 April 2022
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Abstract

The study of specific heat is motivated by the fact that a sudden change in the value of specific heat might be interpreted as a signal of a phase transition. It is also an established fact that multifractal analysis has been proved to be highly effective in characterizing fluctuations which is considered to be important tool for understanding the mechanism of quark-gluon plasma (QGP) in high energy nucleus-nucleus collisions. The Present research work provides some fascinating investigations on multifractal specific heat, c using the concept of entropy, fq which is found as a potential procedure in the study of multifractal specific heat along with the earlier known approaches. The investigations are done for the produced shower particles in nuclear emulsion detector for 28Si-nucleus interactions at 14.5 A GeV/c in the framework of generalized dimension. An attempt is also made to discuss certain universal properties of multifractal specific heat and entropy. We have computed c, by applying the methodology of modified and Takagi moments (Tq). Experimental results are compared with the predictions of LUND model FRITIOF. Moreover, the constant-specific heat method, which is based on the concept of entropy and is commonly accepted in conventional thermodynamics, is demonstrated to be suitable in multifractal thermodynamics also. The values of ‘c’ calculated from these methods are compared with constant specific heat approximations (CSHs) obtained using multifractal entropy (fq). It is found that the values of ‘c’, estimated using Takagi approach are consistent with those of Bershadskii's work as compared to those calculated using (Gam) moments and multifractal entropy, fq. This is obtained for both experimental and for the FRITIOF generated data for the three types of interactions namely, CNO, emulsion and AgBr. The findings of this paper reveal useful information regarding the choice of method used and our results are consistent with CSH approximation for both experimental and simulated data and also in conjunction with recent studies on multifractal specific heat.

Published in American Journal of Modern Physics (Volume 11, Issue 2)
DOI 10.11648/j.ajmp.20221102.14
Page(s) 39-45
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Multiparticle Production, Entropy, Multifractal Specific Heat, Relativistic Nuclear Collisions, Quark-Gluon Plasma, Multifractality

References
[1] H. E. Stanley and P. Meakin, Nature 335, (1988) 405. https://doi.org/10.1038/335405a0
[2] A. Arneodo et al., Physica A 213, (1995) 232. https://doi.org/10.1016/0378-4371(94)00163-N
[3] R. C. Hwa and J. C. Pan, Phys. Rev. D 45, (1992) 1476. https://doi.org/10.1103/PhysRevD.45.1476
[4] R. C. Hwa, Phys. Rev. D 41, (1990) 1456. https://doi.org/10.1103/PhysRevD.41.1456
[5] F. Takagi, Phys. Rev. Lett., 53, (1984) 427. https://doi.org/10.1103/PhysRevLett.53.427
[6] A. Kamal et al., Int, J. Mod. Phys. E 20, (2011) 2269-2292. https://doi.org/10.1142/S0218301311020289
[7] A. Kamal et al., Int. J. Mod. Phys. E 22, (2013) 1350033. https://doi.org/10.1142/S021830131350033X
[8] A. Kamal et al., Int, J. Mod. Phys. E 23, (2014) 1400516. https://doi.org/10.1142/S0218301314500165
[9] Shaista Khan and S. Ahmad, Int, J. Mod. Phys. E 27, (2018) 1850004. https://doi.org/10.1142/S0218301318500040
[10] A. Bershadskii, Physica A 253, (1998) 23-37. https://doi.org/10.1016/S0378-4371(97)00663-8
[11] L. D. Landau and E. M. Lifshitz, Statistical Physics, Part 1, Pergamon Press, Oxford, (1980).
[12] D. Ghosh et al., Nucl. Phys. A 707, (2002) 213-223. https://doi.org/10.1016/S0375-9474(02)00754-6
[13] S. Ahmad et al., Solitons Fractals, 42, (2009) 538-547. https://doi.org/10.1016/j.chaos.2009.01.019
[14] V. Simak et al., Phys. Lett. B 206, issue 1, (1988)159-162 https://doi.org/10.1016/0370-2693(88)91280-4
[15] R. Clausius, The Mechanical Theory of Heat; McMillan and Co.: London, UK, (1879). https://www.worldcat.org/title/mechanical-theory-of-heat/oclc/2162273
[16] L. Boltzmann, Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen. Sitz. Ber. Akad. Wiss. Wien (II) 66, (1872) 275–370.
[17] L. Boltzmann, Über die Beziehung eines allgemeinen mechanischen Satzes zum zweitenHauptsatz der Wärmetheorie. Sitz. Ber. Akad. Wiss. Wien (II) 75, (1877) 67–73.
[18] J. W. Gibbs, Elementary Principles in Statistical Mechanics—Developed with Especial Referencesto the Rational Foundation of Thermodynamics; C. Scribner’s Sons: New York, NY, USA, (1902).
[19] José M. Amigó et al., Entropy, 20(11), (2018) 813. https://doi.org/10.3390/e20110813
[20] C. Shannon, & W. Weaver, The Mathematical Theory of Communication, University of IllinoisPress, Urbana, Chicago, IL & London. (1964).
[21] R. Hartley, ‘Transmission of information’, The Bell System Technical Journal 7, (1928) 535–563.10.1002/j.1538-7305.1928.tb01236.x.
[22] A. R´enyi, On measures of entropy and information, in ‘Proceedings of the Fourth BerkeleySymposium of Mathematical Statistics and Probability’, University of California Press, Berkeley, (1961) pp. 547–561. https://projecteuclid.org/proceedings/berkeley-symposium-on-mathematical-statistics-and-probability/Proceedings-of-the-Fourth-Berkeley-Symposium-on-Mathematical-Statistics-and/Chapter/On-Measures-of-Entropy-and-Information/bsmsp/1200512181
[23] M. M. Khan et al., Indian. J. Phys. 85(1), (2011) 195-199. 10.1007/s12648-011-0040-8.
[24] M. M. Khan et al., Int. J. Mod. Phys. E 21, (2012) 1250068. 10.1142/S0218301312500681.
[25] S. Ahmad et al., "Entropy Analysis in Relativistic Heavy-Ion Collisions", Advances in High EnergyPhysics, Hindawi Publishing Corporation (2013). 10.1155/2013/836071.
[26] S. Khan and S. Ahmad, Int. J. Mod. Phys. E 27, (2018) 1850004. https://doi.org/10.1142/S0218301318500040
[27] S. Pal and S. Pratt, “Entropy production at RHIC,” Physics Letters, B. 578, no. 3, (2004) pp. 310–317.10.1016/j.physletb.2003.10.054.
[28] A. Bialas and W. Czyz, “Event by event analysis and entropy of multiparticle systems,” Physical Review D: Particles, Fields, Gravitation and Cosmology, vol. 61, no. 7, (2000).arXiv:hep-ph/0002140v1.
[29] D. Ghosh, et al., “Entropy scaling in high-energy nucleus–nucleus interactions,” Journal of Physics G: Nuclear and Particle Physics, vol. 38, (2011) 065105. https://iopscience.iop.org/article/10.1088/0954-3899/38/6/065105/meta
[30] A. Bialas, W. Czy˙z, and A. Białas, “Renyi Entropies in Multiparticle Production,” Acta Physica Polonica B, vol. 31, p. (2000) 2803. https://www.actaphys.uj.edu.pl/R/31/12/2803
[31] I. Zborovsky and M. Tokarev, Phys. of Particles & Nuclei Letters, 18, (2021) 302-314. https://doi.org/10.1134/S1547477121030110
[32] S. Bhattacharya et al., Advances in High Energy Physics, vol, 2018, Article ID 6384357. https://doi.org/10.1155/2018/6384357
[33] C. F. Powell et al., The study of Elementary Particles by Photographic Emulsion Methods 450, (Pergamon Press, (1959).
[34] S. Ahmad et al., J. Part. Nucl. Phys. G 30, (2004) 1145. 10.1088/0954-3899/30/9/013.
[35] W. Bari et al., Int. J. Mod. Phys. E 11, (2004) 131. https://doi.org/10.1142/S0218301302000740
[36] S. Ahmad et al., J. Phys. Soc. Jpn. 71, (2002) 1059. 10.1143/JPSJ.71.1059.
[37] Sh. Ahmad and M. Ayaz, J. Physics. G: Nucl. Part. Phys. 32, (2006) 1279-1293 https://doi.org/10.1088/0954-3899/32/9/006
[38] ] P. Mali and A. Mukhopadhyay, Fractals, Vol. 20, No. 3 (2012) 1-13 DOI: 10.1142/S0218348X12500181.
[39] A. Bershadskii, Phys. Rev. C 59, (1999)364-368 DOI: https://doi.org/10.1103/PhysRevC.59.364
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    Arshad Kamal, Mohammad Mohisin Khan. (2022). Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions. American Journal of Modern Physics, 11(2), 39-45. https://doi.org/10.11648/j.ajmp.20221102.14

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    Arshad Kamal; Mohammad Mohisin Khan. Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions. Am. J. Mod. Phys. 2022, 11(2), 39-45. doi: 10.11648/j.ajmp.20221102.14

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    AMA Style

    Arshad Kamal, Mohammad Mohisin Khan. Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions. Am J Mod Phys. 2022;11(2):39-45. doi: 10.11648/j.ajmp.20221102.14

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  • @article{10.11648/j.ajmp.20221102.14,
      author = {Arshad Kamal and Mohammad Mohisin Khan},
      title = {Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions},
      journal = {American Journal of Modern Physics},
      volume = {11},
      number = {2},
      pages = {39-45},
      doi = {10.11648/j.ajmp.20221102.14},
      url = {https://doi.org/10.11648/j.ajmp.20221102.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20221102.14},
      abstract = {The study of specific heat is motivated by the fact that a sudden change in the value of specific heat might be interpreted as a signal of a phase transition. It is also an established fact that multifractal analysis has been proved to be highly effective in characterizing fluctuations which is considered to be important tool for understanding the mechanism of quark-gluon plasma (QGP) in high energy nucleus-nucleus collisions. The Present research work provides some fascinating investigations on multifractal specific heat, c using the concept of entropy, fq which is found as a potential procedure in the study of multifractal specific heat along with the earlier known approaches. The investigations are done for the produced shower particles in nuclear emulsion detector for 28Si-nucleus interactions at 14.5 A GeV/c in the framework of generalized dimension. An attempt is also made to discuss certain universal properties of multifractal specific heat and entropy. We have computed c, by applying the methodology of modified and Takagi moments (Tq). Experimental results are compared with the predictions of LUND model FRITIOF. Moreover, the constant-specific heat method, which is based on the concept of entropy and is commonly accepted in conventional thermodynamics, is demonstrated to be suitable in multifractal thermodynamics also. The values of ‘c’ calculated from these methods are compared with constant specific heat approximations (CSHs) obtained using multifractal entropy (fq). It is found that the values of ‘c’, estimated using Takagi approach are consistent with those of Bershadskii's work as compared to those calculated using (Gam) moments and multifractal entropy, fq. This is obtained for both experimental and for the FRITIOF generated data for the three types of interactions namely, CNO, emulsion and AgBr. The findings of this paper reveal useful information regarding the choice of method used and our results are consistent with CSH approximation for both experimental and simulated data and also in conjunction with recent studies on multifractal specific heat.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Constant Specific Heat Approximation in Multifractal Thermodynamics in Multiparticle Production in Relativistic Heavy-Ion Collisions
    AU  - Arshad Kamal
    AU  - Mohammad Mohisin Khan
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    JF  - American Journal of Modern Physics
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    PB  - Science Publishing Group
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    AB  - The study of specific heat is motivated by the fact that a sudden change in the value of specific heat might be interpreted as a signal of a phase transition. It is also an established fact that multifractal analysis has been proved to be highly effective in characterizing fluctuations which is considered to be important tool for understanding the mechanism of quark-gluon plasma (QGP) in high energy nucleus-nucleus collisions. The Present research work provides some fascinating investigations on multifractal specific heat, c using the concept of entropy, fq which is found as a potential procedure in the study of multifractal specific heat along with the earlier known approaches. The investigations are done for the produced shower particles in nuclear emulsion detector for 28Si-nucleus interactions at 14.5 A GeV/c in the framework of generalized dimension. An attempt is also made to discuss certain universal properties of multifractal specific heat and entropy. We have computed c, by applying the methodology of modified and Takagi moments (Tq). Experimental results are compared with the predictions of LUND model FRITIOF. Moreover, the constant-specific heat method, which is based on the concept of entropy and is commonly accepted in conventional thermodynamics, is demonstrated to be suitable in multifractal thermodynamics also. The values of ‘c’ calculated from these methods are compared with constant specific heat approximations (CSHs) obtained using multifractal entropy (fq). It is found that the values of ‘c’, estimated using Takagi approach are consistent with those of Bershadskii's work as compared to those calculated using (Gam) moments and multifractal entropy, fq. This is obtained for both experimental and for the FRITIOF generated data for the three types of interactions namely, CNO, emulsion and AgBr. The findings of this paper reveal useful information regarding the choice of method used and our results are consistent with CSH approximation for both experimental and simulated data and also in conjunction with recent studies on multifractal specific heat.
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Author Information
  • Department of Physics, Shibli National College, Azamgarh, India

  • Department of Applied Physics, Zakir Husain College of Engineering and Technology, Aligarh Muslim University, Aligarh, India

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