relation: https://pure.iiasa.ac.at/id/eprint/14521/
title: Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches
creator: Hanel, R.
creator: Corominas-Murtra, B.
creator: Thurner, S.
description: 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.
publisher: IOP
date: 2017-03-06
type: Article
type: PeerReviewed
format: text
language: en
rights: cc_by
identifier: https://pure.iiasa.ac.at/id/eprint/14521/1/Hanel_2017_New_J._Phys._19_033008.pdf
identifier:   Hanel, R., Corominas-Murtra, B., & Thurner, S. <https://pure.iiasa.ac.at/view/iiasa/307.html>  (2017).  Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches.   New Journal of Physics 19 (3) e033008. 10.1088/1367-2630/aa611d <https://doi.org/10.1088/1367-2630%2Faa611d>.       
relation: 10.1088/1367-2630/aa611d
identifier: 10.1088/1367-2630/aa611d
doi: 10.1088/1367-2630/aa611d