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The authors investigate, using both analytical and numerical methods, the entropy associated with a diffusion process inside frictional finger patterns. The entropy obtained from simulations of diffusion inside the pattern is compared to analytical predictions based on an effective continuum description. The analytical result predicts that the entropy depends in a particular way on the path dimension of the system, which governs the scaling of simple paths in the system. The findings indicates that there is a close analogy between the frictional fingers in the continuum and minimum spaning trees on the lattice, as the path dimension is found, through studies of the entropy, to be close to the defining value for the minimum spanning tree universality class.

Diffusion Entropy and the Path Dimension of Frictional Finger Patterns