On incomplete statistics and the loop quantum gravity Immirzi parameter

¹ 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
⁴ Departamento de Física, Universidade do Estado do Rio Grande do Norte - 59610-210, Mossoró- RN, Brazil
⁵ Departamento de Física, Universidade do Estado do Rio Grande do Norte - Natal, RN, Brazil

^(a) evertonabreu@ufrrj.br
^(b) jorge@fisica.ufjf.br
^(c) edesiobarboza@uern.br
^(d) brauliosoares@uern.br

Received: 16 April 2019
Accepted: 10 July 2019

Abstract

Incomplete statistics, an important extension of the Boltzmann-Gibbs statistical distribution, was proposed few years back by Wang. The main point is that the formalism adopts an incomplete normalization condition given by , where q is a positive real parameter and p_i is the probability of a determined microstate. In this paper, we have used this framework to derive a new relation between the Immirzi parameter, the q incomplete parameter and the area of a punctured surface. After that, we have compared our result to the Immirzi parameter previously obtained within the context of both Tsallis and Kaniadakis statistics. We have demonstrated in an exact way that the value of the LQG Immirzi parameter can also be calculated using Tsallis, Kaniadakis and incomplete formalisms showing different behaviors, which confirms the distinction property of the parameter.