  We consider, from a dynamical systems point of view, a trivalent spin network
model in Loop Quantum Gravity presenting self-organized criticality (SOC),
arising from a spin propagation dynamics. We obtain a partition function for
the domains of stability connecting gauge non-invariant avalanches, leading to
an entropy formula for the asymptotic SOC state. The microscopic origin of this
SOC entropy is therefore given by the excitation-relaxation spin dynamics in
the avalanche cycle. The puncturing of TSN edges participating in the avalanche
are counted in terms of an ensemble perimeter over the implicit avalanches. By
identifying this perimeter with that of an isolated $(2+1)$-dim. black hole
horizon, we conjecture that the SOC entropy reduces to the Bekenstein-Hawking
perimeter-entropy law for the Ba\~nados, Teitelboim, and Zanelli (BTZ) black
hole, by an appropriate adjustment of a potential function based on the
thermodynamical formalism of Sinai, Ruelle and Bowen.
