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.

arXiv commentPresented in the 2005 Essay Competition of the Gravity Research Foundation. To appear in Int. Jour. of Mod. Phys. A

References in corpus (4)

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• What should a statistical mechanics satisfy to reflect nature?
• Gravity as elasticity of spacetime: a paradigm to understand horizon thermodynamics and cosmological constant
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Cited by in corpus (4)

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• On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric
• The quantum of area $\Delta A=8\pi l_P^2$ and a statistical interpretation of black hole entropy
• Fundamental Constants, Entropic Gravity and Nonextensive Equipartition Theorem