Maximum Entropy and Bayesian Methods

Volume 43 of the series Fundamental Theories of Physics pp 253-264

Energy Flow-Networks and the Maximum Entropy Formalism

  • J. WagensbergAffiliated withDepartment de Física Fonamental
  • , A. GarcíaAffiliated withDepartment de Física Fonamental
  • , R. V. SoléAffiliated withDepartment de Física FonamentalDepartment de Física i Enginyeria Nuclear

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Most natural complex systems can be visualized as a graph of certain preassigned compartments whose nodes are then mutually connected through the internal exchanges of some extensive magnitudes such as material, charge or energy. The Mathematical Theory of Information can be applied to such a graph in order to define two relevant quantities: a measure of connectivity (the joint entropy H of the connections) and a measure of the degree of “energetic” specialization (the internal transfer of information I). A particular kind of evolution is proposed in order to predict the adaptation of such systems towards the observed stationary states. Experimental data concerning the structure of eleven well known energy flow networks in ecology provide some evidence about the reliability of this proposal.