Non-Boltzmann Statistics as an Alternative to Holography

TL;DR

This paper proposes that non-standard, non-Boltzmann statistics could explain the area-scaling of entropy in black hole thermodynamics, potentially eliminating the need for holographic principles.

Contribution

It introduces a novel statistical framework for space-time degrees of freedom that may account for holographic entropy scaling without relying on holography.

Findings

Suggests non-Boltzmann statistics can produce area-law entropy

Provides a new perspective on the microscopic nature of space-time

Offers insights into the role of gravity in statistical correlations

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.