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The entropy production and the variational functional of a Laplaciandiffusional field around the first four fractal iterations of a linearself-similar tree (von Koch curve) is studied analytically and detailedpredictions are stated. In a next stage, these predictions are confronted withresults from numerical resolution of the Laplace equation by means of FiniteElements computations. After a brief review of the existing results, the rangeof distances near the geometric irregularity, the so-called "Near Field", asituation never studied in the past, is treated exhaustively. We notice herethat in the Near Field, the usual notion of the active zone approximationintroduced by Sapoval et al. is strictly inapplicable. The basic new result isthat the validity of the active-zone approximation based on irreversiblethermodynamics is confirmed in this limit, and this implies a newinterpretation of this notion for Laplacian diffusional fields.

Entropy production of entirely diffusional Laplacian transfer and the possible role of fragmentation of the boundaries