Dimensional regularization of Renyi’s statistical mechanics

Plastino, A.; Rocca, Mario Carlos; Ferri, Gustavo Luis

doi:10.1016/j.physa.2018.04.010

Cited by 7 publications

(4 citation statements)

References 36 publications

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“…In 2018 the problem of exponentially divergent nature of gravitational partition function was solved by Plastino and Rocca [48,49,50], thus deserves a special mention in the conclusive section of this paper. General relativity has been thoroughly tested at solar system scale [51], and it is known to be valid at that scale.…”

Section: Discussionmentioning

confidence: 95%

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Gravitational partition function modified by superlight braneworld perturbative modes

et al. 2021

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In this paper, we will analyze the effects of super-light brane world perturbative modes on clustering of galaxies. In present manuscript, we use the Boltzmann and Tsallis statistical approaches to study the large distance modification of gravity in the brane world. The impact of modified potential on clustering of galaxies is analyzed in both the approaches. The infinities associated with Newtonian point mass approximation of gravity models is removed using the analytical extensions. The regularized and finite partition function is obtained for the system of galaxies in the brane world model and is used to evaluate the regularized thermodynamic properties of the system in the form of equations of state. Hence, we study thermodynamic quantities and discuss about the thermodynamic stability of the model. We find that large number of galaxies may lead to the thermodynamic instability. The appealing feature of the paper revolve around the generalization of the dimensional regularization (GDR) of Bollini and Giambiagi supplemented with the statistical adequacy of Boltzmann and Tsallis.

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Section: Discussionmentioning

confidence: 95%

“…The choice of that value of q is not arbitrary. It is the value of q where Verlinde's conjecture of emergent gravity could be proved, in the non-relativistic case [48]. Accordingly:…”

Section: Probability Distribution Functionmentioning

confidence: 99%

Gravitational partition function modified by superlight braneworld perturbative modes

et al. 2021

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“…It was well known that the Boltzmann partition function of gravity could not be calculated because the integral that defines it is exponentially divergent. In 2018 this problem was solved by Plastino and Rocca [39,41,42] by using the generalization of the dimensional regularization of Bollini and Giambiagi [43,44,45]. This generalization was based on the general quantification method of QFT's [46,47,48,49] using Ultradistributions of Sebastiao e Silva, also known as Ultrahyperfunctions [50,51,52].…”

Section: Discussionmentioning

confidence: 99%

Two approaches that prove divergence free nature of non-local gravity

et al. 2021

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This paper is an attempt to study the thermodynamics of the structure formation in the large scale universe in the non local gravity using Boltzmann statistics and the Tsallis statistics. The partition function is obtained in both the approaches and the corresponding thermodynamics properties are evaluated. The important thing about the paper is that we surprisingly get the divergence free integrals and thus stress upon the fact that the nonlocal gravity is the singularity free model of gravity.

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“…So, in this letter we will use the generalization of the dimensional regularization (GDR) [6,7,8,9,10,11] to obtain a finite or divergence free gravitational partition function. This method generalize the dimensional regularization of Bollini and Giambiagi [14,15,16,17,12,13] It may be noted that the entropy obtained from the gravitation partition function has been used to analyze the clustering of galaxies. This has been done by relating the entropy of the system of galaxies to the clustering parameter, and this can in turn be related to the observations [18,19,20,21,22].…”

Section: Introductionmentioning

confidence: 99%

Finite Tsallis Gravitational Partition Function for a System of Galaxies

Hameeda,

Pourhassan,

Rocca

et al. 2021

Preprint

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In this paper, we will study the large scale structure formation using the gravitational partition function. We will assertively argue that the system of gravitating galaxies can be analyzed using the Tsallis statistical mechanics. The divergences in the Tsallis gravitational partition function can be removed using the mathematical riches of the generalization of the dimensional regularization (GDR). The finite gravitational partition function thus obtained will be used to evaluate the thermodynamics of the system of galaxies and thus, to understand the clustering of galaxies in the universe. The correlation function which is believed to contain the information of clustering of galaxies will also be discussed in this formalism.

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Dimensional regularization of Renyi’s statistical mechanics

Cited by 7 publications

References 36 publications

Gravitational partition function modified by superlight braneworld perturbative modes

Gravitational partition function modified by superlight braneworld perturbative modes

Two approaches that prove divergence free nature of non-local gravity

Finite Tsallis Gravitational Partition Function for a System of Galaxies

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