Statistical discrete geometry

Abstract

Following our earlier work [1], we construct statistical discrete geometry by applying statistical mechanics to discrete (Regge) gravity. We propose a coarse-graining method for discrete geometry under the assumptions of atomism and background independence. To maintain these assumptions, we propose restrictions to the theory by introducing cut-offs, both in ultraviolet and infrared regime. Having a well-defined statistical picture of discrete Regge geometry, we take the infinite degrees of freedom (large n) limit. We argue that the correct limit consistent with the restrictions and the background independence concept is not the continuum limit of statistical mechanics, but the thermodynamical limit.

Multi-symplectic Lie Group Thermodynamics for Covariant Field Theories

“…From a broader point of view, the application of our covariant statistical mechanics formalism to discrete gravity models may provide interesting insights to the study of coarse-graining approaches and the continuum limit from a thermodynamical perspective, as initiated for instance in [84,85].…”