eprintid: 14521 rev_number: 12 eprint_status: archive userid: 353 dir: disk0/00/01/45/21 datestamp: 2017-04-05 07:04:52 lastmod: 2021-08-27 17:41:50 status_changed: 2017-04-05 07:04:52 type: article metadata_visibility: show creators_name: Hanel, R. creators_name: Corominas-Murtra, B. creators_name: Thurner, S. creators_id: 1918 title: Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches ispublished: pub divisions: prog_asa abstract: 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. date: 2017-03-06 date_type: published publisher: IOP id_number: 10.1088/1367-2630/aa611d creators_browse_id: 307 full_text_status: public publication: New Journal of Physics volume: 19 number: 3 pagerange: e033008 refereed: TRUE issn: 1367-2630 projects: multi-LAyer SpAtiotemporal Generalized NEtworks (LASAGNE, FP7 318132) projects: Foundational Research on MULTIlevel comPLEX networks and systems (MULTIPLEX, FP7 317532) coversheets_dirty: FALSE fp7_project: yes fp7_project_id: info:eu-repo/grantAgreement/EC/FP7/318132/EU//LASAGNE; info:eu-repo/grantAgreement/EC/FP7/317532/EU//MULTIPLEX fp7_type: info:eu-repo/semantics/article access_rights: info:eu-repo/semantics/openAccess citation: Hanel, R., Corominas-Murtra, B., & Thurner, S. (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 . document_url: https://pure.iiasa.ac.at/id/eprint/14521/1/Hanel_2017_New_J._Phys._19_033008.pdf