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Keywords = calculus Tsallis 60E99

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15 pages, 838 KB  
Article
Aspects of Quantum Statistical Mechanics: Fractional and Tsallis Approaches
by Ervin Kaminski Lenzi, Luiz Roberto Evangelista and Luciano Rodrigues da Silva
Mathematics 2023, 11(12), 2777; https://doi.org/10.3390/math11122777 - 20 Jun 2023
Cited by 1 | Viewed by 1863
Abstract
We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of [...] Read more.
We investigated two different approaches, which can be used to extend the standard quantum statistical mechanics. One is based on fractional calculus, and the other considers the extension of the concept of entropy, i.e., the Tsallis statistics. We reviewed and discussed some of the main properties of these approaches and used the thermal Green function formalism to perform the developments, simultaneously allowing us to analyze each case’s dynamics and thermodynamics aspects. In particular, the results allow us to understand how the extensions change the behavior of some quantities, particularly fluctuations related to the system. Full article
(This article belongs to the Section E4: Mathematical Physics)
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7 pages, 253 KB  
Article
q-Functions and Distributions, Operational and Umbral Methods
by Giuseppe Dattoli, Silvia Licciardi, Bruna Germano and Maria Renata Martinelli
Mathematics 2021, 9(21), 2664; https://doi.org/10.3390/math9212664 - 21 Oct 2021
Cited by 1 | Viewed by 2573
Abstract
The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral [...] Read more.
The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials. These methods have helped to frame either elementary and special functions within the same logical context. Methods of Umbral and operational calculus have been embedded in a powerful and efficient analytical tool, which will be applied to the study of the properties of distributions such as Tsallis, Weibull and Student’s. We state that they can be viewed as standard Gaussian distributions and we take advantage of the relevant properties to infer those of the aforementioned distributions. Full article
(This article belongs to the Special Issue Advances in Functional Equations and Convex Analysis)
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