Black-hole entropy and minimal diffusion

Abstract

The density of states reproducing the Bekenstein-Hawking entropy-area scaling can be modeled via a nonlocal field theory. We define a diffusion process based on the kinematics of this theory and find a spectral dimension whose flow exhibits surprising properties. While it asymptotes four from above in the infrared, in the ultraviolet the spectral dimension diverges at a finite (Planckian) value of the diffusion length, signaling a breakdown of the notion of diffusion on a continuum spacetime below that scale. We comment on the implications of this minimal diffusion scale for the entropy bound in a holographic and field-theoretic context.

5 pages, 1 figure. v2: physical interpretation of the results clarified

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• ABC of multi-fractal spacetimes and fractional sea turtles
• Quantum spectral dimension in quantum field theory
• Standard Model in multiscale theories and observational constraints
• Particle-physics constraints on multifractal spacetimes
• UV dimensional reduction to two from group valued momenta
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• Three-dimensional gravity and deformations of relativistic symmetries
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