Self‐organization in hierarchically organized systems

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Abstract
Firstly, we study dynamical processes in a hierarchically organized set of interacting elements. We study inter‐levels couplings which can be of two types, bottom‐top and top‐bottom. We apply this general method to coupled individual and population dynamics in Ecology. We realize computer simulations of this example. The coupling between the two levels gives birth to nonlinear effects. Secondly, we study thermodynamical aspects and we show that the entropy of a hierarchically organized system is the sum of entropies associated to each of the hierarchical levels. We consider ensembles with equiprobable and non equiprobable states. These states probabilities are calculated from the transition graph of the dynamical model. In this way, we relate thermodynamical models of hierarchically organized systems to dynamical models. Then, we calculate the entropy variation resulting from a change in the transition graph of the dynamical model. We show that the entropy of a hierarchically organized system can be larger than the entropy of a non hierarchical system.