An expression of the hydrologic response of fractal networks is derived by means of the classical approach used in statistical-mechanics. Probabilities of the rate of arrivals at the outlet of mass particles instantaneously injected into the network are maximized accounting for some suitable constraints. The analysis of the structure of fractal networks allows us to meaningfully set the required constraints, that are of the same form of these used by Lienhard and Meyer (1967). The resulting hydrologic response is a Weibull distribution whose parameters are the fractal dimension and the total length of the network. A comparison with the similar form of arrival time distribution obtained by Troutman and Karlinger (1985) showed it to be a particular case of the more general expression relative to fractal networks.
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