The Gentile statistics interpolates between the standard bosonic and fermionic statistics, allowing an intermediate maximum state occupation 1< M < ∞. A generalization of this statistics having the Gibbs factor phenomenologically substituted with the nonadditive Tsallis q-exponential is analyzed. Depending on the values of the statistics parameter q, peculiarities of the thermodynamic functions are observed: for q > 1, a finite (nonzero) minimum temperature arises in the model, while for q < 1, the specific heat does not tend to zero at T → 0. These results are consistent with previously reported for a similar generalization of the fermionic statistics [A. Rovenchak and B. Sobko, Physica A 534, 122098 (2019)]. Their relevance for modeling phenomena in real physical systems is briefly outlined.
REFERENCES
1.
S.
Bose
, “Plancks Gesetz und Lichtquantenhypothese
,” Zs.Phys.
26
(1
), 178
(1924
). 2.
A.
Einstein
, “Quantentheorie des einatomigen idealen Gases
,” Sitzungsber Preuss. Konigl. Akad. Wiss.: Phys.-Math. Klasse
1924
, 261
.3.
A.
Einstein
, “Quantentheorie des einatomigen idealen Gases, zweite Abhandlung
,” Sitzungsber. Preuss. Konigl. Akad. Wiss.: Phys.-Math. Klasse
1925, 3.4.
E.
Fermi
, “Zur Quantelung des idealen einatomigen Gases,
” Zs. Phys.
36
, No. 11–12
, 902
(1926
). 5.
P. A. M.
Dirac
, “On the theory of quantum mechanics
,” Proc. R. Soc. London Ser. A
112
, 661
(1926
). 6.
G.
Gentile
, Jr., “Osservazioni sopra le statistiche intermedie
,” Nuovo Cim.
17
, 493
(1940
). 7.
G.
Gentile j
., “Le statistiche intermedie e le proprietà dell’elio liquido
,” Nuovo Cim. Nuova Ser.
19
, No. 4
, 109
(1942
). 8.
9.
R.
Ramanathan
, “Further aspects of an interpolative quantum statistics,
” Phys. Rev. E
48
, No. 2
, 843
(1993
). 10.
O. W.
Greenberg
, “Interactions of particles having small violations of statistics
,” Physica A
180
, 419
(1992
). 11.
O. W.
Greenberg
, “Theories of violation of statistics
,” AIP Conf. Proc.
545
, 113
(2000
). 12.
S.
Selvi
and H.
Uncu
, “A new method for derivation of statistical weight of the gentile statistics
,” Physica A
436
, 739
(2015
). 13.
W
. S.
Chung
and H.
Hassanabadi
, “f-deformed boson algebra related to Gentile statistics
,” Int. J. Theor. Phys.
56
, 1746
(2017
). 14.
W. S.
Chung
and H.
Hassanabadi
, “On the p-deformed fermion algebra: Thermodynamics of p-fermion gas
,” Ann. Phys.
386
, 242
(2017
). 15.
Y.
Shen
and F.-L.
Zhang
, “Intermediate symmetric construction of transformation between anyon and Gentile statistics
,” Commun. Theor. Phys.
73
, 065601
(2021
). 16.
Y.
Shen
, Ch.-Ch.
Zhou
, and Y-Zh.
Chen
, “The elementary excitation of spin lattice models The quasiparticles of Gentile statistics
,” Physica A
596
, 127223
(2022
). 17.
A.
Rovenchak
, “Ideal Bose-gas in nonadditive statistics
,” Fiz. Nizk. Temp.
44
, 1308
(2018
) [Low Temp. Phys.
44, 1025 (2018)]. 18.
A.
Rovenchak
and B.
Sobko
, “Fugacity versus chemical potential in nonadditive generalizations of the ideal Fermi-gas
,” Physica A
534
, 122098
(2019
). 19.
B.
Sobko
and A.
Rovenchak
, “Superadditive model of the ideal Fermi-gas near absolute zero
,” Visn. Lviv Univ. Ser. Phys.
56
, 65
(2019
). 20.
E.
Lutz
and F.
Renzoni
, “Beyond Boltzmann-Gibbs statistical mechanics in optical lattices
,” Nature Phys.
9
, 615
(2013
). 21.
D.
Gribben
, D. M.
Rouse
, J.
Iles-Smith
, A.
Strathearn
, H.
Maguire
, P.
Kirton
, A.
Nazir
, E. M.
Gauger
, and B. W.
Lovett
, “Exact dynamics of nonadditive environments in non-Markovian open quantum systems
,” PRX Quantum
3
, 010321
(2022
). 22.
M.
Irshad
, M.
Khalid
, and Ata-ur-
Rahman
, “Modulational instability of ion acoustic excitations in a plasma with a κ-deformed Kaniadakis electron distribution
,” Eur. Phys. J. Plus
137
, No. 8
, 1
(2022
). 23.
R.
D’Agostino
, “Holographic dark energy from nonadditive entropy: Cosmological perturbations and observational constraints
,” Phys. Rev. D
99
, 103524
(2019
). 24.
A.
Alonso-Serrano
, M. P.
Dabrowski
, and H.
Gohar
, “Nonextensive black hole entropy and quantum gravity effects at the last stages of evaporation
,” Phys. Rev. D
103
, 026021
(2021
). 25.
P.
Jizba
and G.
Lambiase
, “Tsallis cosmology and its applications in dark matter physics with focus on IceCube high-energy neutrino data
,” Eur. Phys. J. C
82
, 1123
(2022
). 26.
A.
Ramirez-Arellano
, L.
Manuel Hernández-Simón
, and J.
Bory-Reyes
, “A box-covering tsallis information dimension and non-extensive property of complex networks, chaos
,” Solitons & Fractals
132
, 109590
(2020
). 27.
R. M.
de Oliveira
, S.
Brito
, L. R.
da Silva
, and C.
Tsallis
, “Connecting complex networks to nonadditive entropies
,” Sci. Rep.
11
, 1130
(2021
). 28.
M. A.
Montemurro
, A Generalization of the Zipf-Mandelbrot Law in Linguistics, in Nonextensive Entropy Interdisciplinary Applications
, edited by Murray Gell-Mann and Constantino Tsallis (Oxford University Press
, 2004
), p. 347
.29.
Y.
Liu
, Ch.-Y.
Yu
, and K.-M.
Shen
, “Researches on the COVID-19 epidemic in the world within a nonextensive SIR model
,” Med. Res. Arch.
(published online 2022).30.
C.
Tsallis
, “What are the numbers that experiments provide?
” Qu쬩ca Nova
17
, 468
(1994
).31.
C.
Ou
and J.
Chen
, “Thermostatistic properties of a q-generalized Bose system trapped in an n-dimensional harmonic oscillator potential
,” Phys. Rev. E
68
, 026123
(2003
). 32.
T.
Yamano
, “Some properties of q-logarithm and q-exponential functions in tsallis statistics
,” Physica A
305
, 486
(2002
). 33.
L.
Salasnich
, “BEC in nonextensive statistical mechanics
,” Int. J. Mod. Phys. B
14
, 405
(2000
). 34.
W.-S.
Dai
and M.
Xie
, “Gentile statistics with a large maximum occupation number
,” Ann. Phys. (N. Y.
) 309
, 295
(2004
). 35.
W.-S.
Dai
and M.
Xie
, “Do bosons obey Bose-Einstein distribution: Two iterated limits of Gentile distribution
,” Phys. Lett. A
373
, 1524
(2009
). 36.
A. I.
Bugrij
and V. M.
Loktev
, “On the theory of ideal Bose-gas
,” Fiz. Nizk. Temp.
47
, 132
(2021
) [Low Temp. Phys.
47, 116 (2021)]. 37.
A. I.
Bugrij
and V. M.
Loktev
, “On the features of ideal Bose-gas thermodynamic properties at a finite particle number
,” Ukr. J. Phys.
67
, 235
(2022
). 38.
Hypergeometric2F1
. URL https://functions.wolfram.com/HypergeometricFunctions/Hypergeometric2F1/, cited on 16 January 2023
.39.
A. A.
Rovenchak
, Exotic Statistics
, (Lviv University Press
, Lviv
, 2018
) ISBN 978-617-10-0461-0.40.
M. H.
Anderson
, J. N.
Ensher
, M. R.
Matthews
, C. E.
Wieman
, and E. A.
Cornell
, “Observation of Bose-Einstein condensation in a dilute atomic vapor
,” Science
269
, 198
(1995
). 41.
V. E.
Syvokon
and S. S.
Sokolov
, “Melting of twodimensional electron clusters in a magnetic field
,” Fiz. Nizk. Temp.
49
, 50
(2023
) [Low Temp. Phys.
49, 46 (2023)]. 42.
J. C.
Mauro
, R. J.
Loucks
, and S.
Sen
, “Heat capacity, enthalpy fluctuations, and configurational entropy in broken ergodic systems
,” J. Chem. Phys.
133
, 164503
(2010
). 43.
L.
Bovo
, X.
Moya
, D.
Prabhakaran
, Y.-A.
Soh
, A.T.
Boothroyd
, N.D.
Mathur
, G.
Aeppli
, and S.T.
Bramwell
, “Restoration of the third law in spin ice thin films
,” Nature Commun.
5
, 3439
(2014
). 44.
M. H.
Mohammady
and T.
Miyadera
, “Quantum measurements constrained by the third law of thermodynamics
,” Phys. Rev. A
107
, 022406
(2023
). 45.
F.
Capela
and P. G.
Tinyakov
, “Black hole thermodynamics and massive gravity
,” J. High En. Phys.
2011
, 42. 46.
H.
Moradpour
, A. H.
Ziaie
, I. P.
Lobo
, J. P.
Morais Graça
, U. K.
Sharma
, and A.
Sayahian Jahromi
, “The third law of thermodynamics, non-extensivity and energy definition in black hole physics
,” Mod. Phys. Lett. A
37
, 2250076
(2022
). 47.
E. P.
Bento
, G. M.
Viswanathan
, M. G. E.
da Luz
, and R.
Silva
, “Third law of thermodynamics as a key test of generalized entropies
,” Phys. Rev. E
91
, 022105
(2015
). 48.
R.
De Pietri
, A.
Feo
, E.
Seiler
, and I.-O.
Stamatescu
, “A model for QCD at high density and large quark mass
,” Phys. Rev. D
76
, 114501
(2007
). 49.
M. M.
Stetsko
, “Microscopic black hole and uncertainty principle with minimal length and momentum
,” Int. J. Mod. Phys. A
28
, 1350029 (2013
). 50.
B.
Hamil
and B. C.
Lutfuoglu
, “Effect of Snyder-de Sitter model on the black hole thermodynamics in the context of rainbow gravity
,” Int. J. Geom. Meth. Mod. Phys.
19
, 2250047
(2022
). 51.
C.
Quesne
and V. M.
Tkachuk
, “Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
,” J. Phys. A
36
, 10373
(2003
). 52.
T. V.
Fityo
, I. O.
Vakarchuk
, and V. M.
Tkachuk
, “The WKB approximation in the deformed space with the minimal length and minimal momentum
,” J. Phys. A
41
, 045305
(2008
). 53.
W. S.
Chung
and H.
Hassanabadi
, “Statistical physics when the minimum temperature is not absolute zero
,” Mod. Phys. Lett. B
32
, 1850123
(2018
). 54.
B.
Sobko
and A.
Rovenchak
, “Effective modeling of physical systems with fractional statistics
,” Fiz. Nizk. Temp.
48
, 702
(2022
) [Low Temp. Phys.
48, 621 (2022)]. 55.
A. M.
Gavrilik
and Yu. A.
Mishchenko
, “Composite fermions as deformed oscillators: Wavefunctions and entanglement
,” Ukr. J. Phys.
64
, 1134
(2019
). 56.
B.
Vitoriano
, R. R.
Montenegro-Filho
, and M. D.
Coutinho-Filho
, “Fractional exclusion statistics and thermodynamics of the hubbard chain in the spin-incoherent Luttinger liquid regime
,” Phys. Rev. B
98
, 085130
(2018
). © 2023 Author(s). Published under an exclusive license by AIP Publishing.
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