Non-Boltzmann Statistics as an Alternative to Holography

Abstract

An intriguing question related to black hole thermodynamics is that the entropy of a region shall scale as the area rather than the volume. In this essay we propose that the microscopical degrees of freedom contained in a given region of space, are statistically related in such a way that obey a non-standard statistics, in which case an holographic hypothesis would be not needed. This could provide us with some insight about the nature of degrees of freedom of the geometry and/or the way in which gravitation plays a role in the statistic correlation between the degrees of freedom of a system. 1 botta@cbpf.br 2

Fundamental constants, entropic gravity and nonextensive equipartition theorem

“…For q = 5/3 we have f = 0 and, consequently, l diverges (l → ∞). It is important to stress that although f varies with the nonextensive parameter It is important to mention here that Cantcheff and Nogales [18] have written the Tsallis' entropy in the form…”

New bounds for Tsallis parameter in a noncommutative phase–space entropic gravity and nonextensive Friedmann equations

“…This result shows us that q = 5/3 is an upper bound limit when we are dealing with the holographic screen. Notice that this approach is different from the one demonstrated in [29], where the authors considered in their model that the number of states is proportional to the volume and not to the area of the holographic screen. These last considerations motivates us to present a preliminary calculation of the qbound.…”

“…It is also easy to observe that for q = 1, the classical equipartition theorem for each microscopic degrees of freedom is recovered. As another path, it is worth to mention that in [29] the authors obtained that Tsallis entropy can be written as…”

“…As another path, it is worth to mention that in [29] the authors obtained that Tsallis entropy can be written as…”

Notes on microstates, Tsallis statistics and entropic gravity formalism

“…One can think that this result connects the thermodynamical Bekenstein-Hawking formula for black holes with the classical Newton's expression for gravity, which could suggest a thermodynamical emergent gravitation. On the other hand, Botta Cantcheff and Nogales [16] have shown that we can derive the usual entropy of black holes by using a volume microstates scaling law (3) and the Tsallis' nonextensive entropy (2). For q = 1 (BG) scenario and same b we have that…”