Volume 124, Number 3, November 2018
|Number of page(s)||6|
|Published online||05 December 2018|
Tsallis' entropy, modified Newtonian accelerations and the Tully-Fisher relation
1 Grupo de Física Teórica e Matemática Física, Departamento de Física, Universidade Federal Rural do Rio de Janeiro 23890-971, Seropédica, RJ, Brazil
2 Departamento de Física, Universidade Federal de Juiz de Fora - 36036-330, Juiz de Fora, MG, Brazil
3 Programa de Pós-Graduação Interdisciplinar em Física Aplicada, Instituto de Física, Universidade Federal do Rio de Janeiro - 21941-972, Rio de Janeiro, RJ, Brazil
Received: 13 August 2018
Accepted: 5 November 2018
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 dependence 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. We have used this new relation to derive three Newtonian-type accelerations in the context of Tsallis' statistics which are a modified gravitational acceleration, a modified MOND theory and a modified Friedmann equation. Moreover we have obtained a nonextensive version of the Tully-Fisher (TF) relation which shows a dependence of the distance of the star in contrast to the standard TF expression. The BG limit gives the standard TF law.
PACS: 05.20.-y – Classical statistical mechanics / 98.65.Cw – Galaxy clusters / 51.10.+y – Kinetic and transport theory of gases
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