  The entropy production and the variational functional of a Laplacian
diffusional field around the first four fractal iterations of a linear
self-similar tree (von Koch curve) is studied analytically and detailed
predictions are stated. In a next stage, these predictions are confronted with
results from numerical resolution of the Laplace equation by means of Finite
Elements computations. After a brief review of the existing results, the range
of distances near the geometric irregularity, the so-called "Near Field", a
situation never studied in the past, is treated exhaustively. We notice here
that in the Near Field, the usual notion of the active zone approximation
introduced by Sapoval et al. is strictly inapplicable. The basic new result is
that the validity of the active-zone approximation based on irreversible
thermodynamics is confirmed in this limit, and this implies a new
interpretation of this notion for Laplacian diffusional fields.
