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Dissipation in Laplacian fields across irregular boundaries.

The entropy production associated to a Laplacian field distributed across irregular boundaries is studied. In the context of the active zone approximation an explicit expression is given for the entropy production in terms of geometry, whose relation to the variational formulation is discussed. It is shown that the entropy production diminishes for successive prefractal generations of the same fractal generator, so that the final fractal object is expected to dissipate less than all previous ones. The relevance of this result in the abundance of fractal surfaces or interfaces observed in nature is discussed.