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We consider, from a dynamical systems point of view, a frozen, planartrivalent spin network model in Loop Quantum Gravity (LQG) presentingself-organized criticality (SOC). We obtain a partition function for thedomains of stability connecting gauge non-invariant avalanches, leading to anentropy formula for the asymptotic SOC state. We use this formalism to obtainthe entropy of a $(2+1)$-dimensional (BTZ) black hole, and conjecture that thisentropy reduces to the Bekenstein-Hawking entropy law by an appropriateadjustment of a potential function.

Ergodic Concepts for a Self-Organizing Trivalent Spin Network