<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches"^^ . "Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent processes. Their statistics is typically non-multinomial in the sense that the multiplicities of the occurrence of states is not a multinomial factor. The maximum entropy principle is tightly related to multinomial processes, non-interacting systems, and to the ensemble picture; it loses its meaning for path-dependent processes. Here we show that an equivalent to the ensemble picture exists for path-dependent processes, such that the non-multinomial statistics of the underlying dynamical process, by construction, is captured correctly in a functional that plays the role of a relative entropy. We demonstrate this for self-reinforcing Pólya urn processes, which explicitly generalize multinomial statistics. We demonstrate the adequacy of this constructive approach towards non-multinomial entropies by computing frequency and rank distributions of Pólya urn processes. We show how microscopic update rules of a path-dependent process allow us to explicitly construct a non-multinomial entropy functional, that, when maximized, predicts the time-dependent distribution function."^^ . "2017-03-06" . . . "19" . "3" . . "IOP"^^ . . . "New Journal of Physics"^^ . . . "13672630" . . . . . . . . . . . . . "B."^^ . "Corominas-Murtra"^^ . "B. Corominas-Murtra"^^ . . "S."^^ . "Thurner"^^ . "S. Thurner"^^ . . "R."^^ . "Hanel"^^ . "R. Hanel"^^ . . . . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Text)"^^ . . . . . . "Hanel_2017_New_J._Phys._19_033008.pdf"^^ . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Other)"^^ . . . . . . "indexcodes.txt"^^ . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Other)"^^ . . . . . . "preview.jpg"^^ . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Other)"^^ . . . . . . "medium.jpg"^^ . . . "Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #14521 \n\nUnderstanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches\n\n" . "text/html" . .