Thermofractals
Thermofractal is a class of thermodynamic systems presenting a fractal structure in its thermodynamic description in the following sense:
- The total energy is given by U=F+E, where F corresponds to the kinetic energy of N' constituent subsystems and E corresponds to the internal energy of those subsystems, which behaves as particles with an internal structure.
- (Only for Type-I) The constituent particles are thermofractals. The ratio ⟨E⟩/⟨F⟩ is constant for all the subsystems. However the ratio E/F can vary according to a distribution, P(E), which is self-similar (self-affine), that is, at different levels of the subsystem hierarchy the distribution of the internal energy are equal (proportional) to those in the other levels.
- (Only for Type-II) The constituent particles are thermofractals. The ratio ⟨E⟩/⟨U⟩ is constant for all the subsystems. However the ratio E/U can vary according to a distribution, P(E), which is self-similar (self-affine), that is, at different levels of the subsystem hierarchy the distribution of the internal energy are equal (proportional) to those in the other levels.
- At some level $n$ in the hierarchy of subsystems the phase space is so narrow that one can consider P(E_n) dEn=ρ dEn, with ρ being independent of the energy En.
It is related to the Non Extensive Self-Consistent Thermodynamics and leads to the Tsallis non-extensive thermodynamics. The concept of thermofractals was introduced in 2016.[1], with just thermofractals of type-I. Later, it was shown that Yang-Mills Quantum Fields can present a fractal structure[2] that presents the same features shown by thermofractals of type-II. It can be shown that thermofractals of Type-I follow the q-exponential function without cut-off, while thermofractals of type-II follow the q-exponential with cut-off.
Thermofractals is a system in many aspects similar to the fireballs, a concept introduced by Rolf Hagedorn to explain the results of high energy collisions. With thermofractals, however, Tsallis statistics emerges in the system, and a complete description of the high energy data can be obtained through the non extensive self-consistent thermodynamics. The connections between thermofractals and fireballs can be found in Ref.[2][3][4]
References
- ↑ Deppman, A. (2016-03-01). "Thermodynamics with fractal structure, Tsallis statistics, and hadrons". Physical Review D. 93 (5): 054001. arXiv:1601.02400. Bibcode:2016PhRvD..93e4001D. doi:10.1103/PhysRevD.93.054001. Unknown parameter
|s2cid=ignored (help) - ↑ 2.0 2.1 Deppman, Airton; Megías, Eugenio; Menezes, Debora P. (2020-02-19). "Fractals, nonextensive statistics, and QCD". Physical Review D. 101 (3): 034019. arXiv:1908.08799. Bibcode:2020PhRvD.101c4019D. doi:10.1103/PhysRevD.101.034019. ISSN 2470-0010. Unknown parameter
|s2cid=ignored (help) - ↑ Deppman, Airton (September 2017). "Fractal Structure of Hadrons: Experimental and Theoretical Signatures". Universe. 3 (3): 62. Bibcode:2017Univ....3...62D. doi:10.3390/universe3030062.
- ↑ Deppman, Airton; Frederico, Tobias; Megías, Eugenio; Menezes, Debora P. (September 2018). "Fractal Structure and Non-Extensive Statistics". Entropy. 20 (9): 633. arXiv:1801.01160. Bibcode:2018Entrp..20..633D. doi:10.3390/e20090633. Unknown parameter
|s2cid=ignored (help)
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