"14521","12","archive","353",,,"disk0/00/01/45/21","2017-04-05 07:04:52","2021-08-27 17:41:50","2017-04-05 07:04:52","article",,,"show","","",,,,"Hanel","R.","","",,"","",,,,,"","","Understanding frequency distributions of path-dependent processes with non-multinomial maximum entropy approaches","pub","","","prog_asa",,,"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","published","IOP","10.1088/1367-2630/aa611d",,,,,,"",,,,,"",,,,,"",,,,,"","",,"",,,,,,,"307","public",,,,"New Journal of Physics","19","3",,"e033008",,,,,,,,,,,"TRUE",,"1367-2630",,,,,,"","","","",,"","multi-LAyer SpAtiotemporal Generalized NEtworks (LASAGNE, FP7 318132)",,,,,,,"",,,,,"FALSE","yes","info:eu-repo/grantAgreement/EC/FP7/318132/EU//LASAGNE; info:eu-repo/grantAgreement/EC/FP7/317532/EU//MULTIPLEX","info:eu-repo/semantics/article","info:eu-repo/semantics/openAccess"
"14521",,,,,,,,,,,,,,,,,,,"Corominas-Murtra","B.","","",,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,"Foundational Research on MULTIlevel comPLEX networks and systems (MULTIPLEX, FP7 317532)",,,,,,,,,,,,,,,,
"14521",,,,,,,,,,,,,,,,,,,"Thurner","S.","","","1918",,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,