Temperature-Dependent Specific Heat of a Monoatomic Gas Based on a Stretched Exponential Partition Function
DOI:
https://doi.org/10.5540/03.2026.012.01.0338Palavras-chave:
Stretched Exponential, Monoatomic Gases, Specific HeatResumo
Accurate modeling of complex systems often requires the application of advanced mathematical tools. In this work, we investigate the thermodynamic behavior of monoatomic gases using a stretched exponential probability density function. By constructing the partition function Z within this framework, we derive expressions for the internal energy and temperature-dependent specific heat of the system. The results are shown to be consistent with classical kinetic theory for ideal gases. Furthermore, comparisons with experimental data are presented, highlighting the viability of this approach.
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Referências
E. Ben-Naim and P. L. Krapivsky. “The inelastic Maxwell model”. In: Granular Gas Dynamics. Berlin: Springer, 2003, pp. 65–94.
K. Górska, A. Horzela, K. A. Penson, G. Dattoli, and G. H. E. Duchamp. “The stretched exponential behavior and its underlying dynamics. The phenomenological approach”. In: Fractional Calculus and Applied Analysis 20.1 (2017), pp. 260–283.
J. Laherrere and D. Sornette. “Stretched exponential distributions in nature and economy: ‘fat tails’ with characteristic scales”. In: The European Physical Journal B-Condensed Matter and Complex Systems 2.4 (1998), pp. 525–539.
S. Luding. “Structures and non-equilibrium dynamics in granular media”. In: Comptes Rendus Physique 3.2 (2002), pp. 153–161.
J.-R. Luévano. “Statistical features of the stretched exponentials densities”. In: Journal of Physics: Conference Series. Vol. 475. 1. IOP Publishing. 2013, p. 012008.
A. Lukichev. “Physical meaning of the stretched exponential Kohlrausch function”. In: Physics Letters A 383.24 (2019), pp. 2983–2987.
R. A. Magomedov, R. R. Meilanov, R. P. Meilanov, E. N. Akhmedov, V. D. Beybalaev, and A. A. Aliverdiev. “Generalization of thermodynamics in of fractional-order derivatives and calculation of heat-transfer properties of noble gases”. In: Journal of Thermal Analysis and Calorimetry 133.2 (2018), pp. 1189–1194.
B. A. Mamedov, E. Somuncu, and I. M. Askerov. “Evaluation of speed of sound and specific heat capacities of real gases”. In: Journal of Thermophysics and Heat Transfer 32.4 (2018), pp. 984–998.
H. Maruoka, A. Nishimura, M. Yoshida, and K. Hatada. “Shannon entropy analysis of the stretched exponential process: application to various shear induced multilamellar vesicles system”. In: arXiv preprint arXiv:1612.07502 (2016).
A. Plastino and M. C. Rocca. “Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs’ statistical mechanics”. In: Physical Review E 95.6 (2017), p. 062110.
A. Plastino and M. C. Rocca. “Tsallis’ quantum q-fields”. In: Chinese Physics C 42.5 (2018), p. 053102.
Y. Shokef. Thermodynamic Analogies in Granular Materials. Haifa: Technion–Israel Institute of Technology, Department of Physics, 2006.
M. O. Vlad, R. Metzler, T. F. Nonnenmacher, and M. C. Mackey. “Universality classes for asymptotic behavior of relaxation processes in systems with dynamical disorder: Dynamical generalizations of stretched exponential”. In: Journal of Mathematical Physics 37.5 (1996), pp. 2279–2306.
