Tsallis and Kaniadakis statistics from a point of view of the holographic equipartition law

In this work, we have illustrated the difference between both Tsallis and Kaniadakis entropies through cosmological models obtained from the formalism proposed by Padmanabhan, which is called holographic equipartition law. Similarly to the formalism proposed by Komatsu, we have obtained an extra driving constant term in the Friedmann equation if we deform the Tsallis entropy by Kaniadakis' formalism. We have considered initially Tsallis entropy as the Black Hole (BH) area entropy. This constant term may lead the universe to be in an accelerated mode. On the other hand, if we start with the Kaniadakis entropy as the BH area entropy and then by modifying the Kappa expression by Tsallis' formalism, the same constant, which shows that the universe have an acceleration is obtained. In an opposite limit, no driving inflation term of the early universe was derived from both deformations.Comment: 8 pages, preprint format. Final version to appear in Europhysics Letter

Upper limits to absorption enhancement in thick solar cells using diffraction gratings

The application of diffraction gratings to solar cells is a promising approach to superseding the light trapping limits of conventional Lambertian structures. In this paper a mathematical formalism is derived for calculating the absorption that can be expected in a solar cell equipped with a diffraction grating, which can be applied to any lattice geometry and grating profile. Furthermore, the formalism is used to calculate the upper limit of total absorption that can theoretically be achieved using a diffraction grating. The derived formalism and limits are valid when the solar cell thickness is greater than the coherence length of the illuminating solar spectrum. Comparison is made to the upper limit achievable using an angularly selective Rugate filter, which is also calculated. Both limits are found to be considerably higher than the Lambertian limit within the range of sunlight concentration factors practically employed in photovoltaic systems (1–1000×). The upper limit of absorption using the diffraction grating is shown to be equal to the thermodynamic limit for all absorbances and concentration factors. The limit for the Rugate filter is generally lower, but tends to the thermodynamic limit for lower cell absorbance

Tsallis' entropy, modified Newtonian accelerations and the Tully-Fisher relation

In this paper we have shown that the connection between the number of bits and the area of the holographic screen, where both were established in Verlinde's theory of entropic gravity, may depend on the thermostatistics theory previously chosen. Starting from the Boltzmann-Gibbs (BG) theory, we have reobtained the usual dependency of both, bits number and area. After that, using Tsallis' entropy concept within the entropic gravity formalism, we have derived another relation between the bits number and the holographic screen area. Moreover, we have used this new relation to derive three Newtonian-type accelerations in the context of Tsallis' statistics. Moreover, we have used this new relation to derive three Newtonian-type acceleration in the context of Tsallis statistics which are a modified gravitational acceleration, a modified MOND theory and a modified Friedmann equation. We have obtained the nonextensive version of the Tully-Fisher (TF) relation which shows a dependency of the distance of the star in contrast to the standard TF expression. The BG limit gives the standard TF law.Comment: 12 pages. Preprint forma

Finite group actions on reductive groups and buildings and tamely-ramified descent in Bruhat-Tits theory

The purpose of the paper is to give a new approach to tamely-ramified descent in Bruhat-Tits theory. This descent was first studied by Guy Rousseau in his thesis.Comment: 28 pages. arXiv admin note: text overlap with arXiv:1611.0743