Altaner, B., Grosskinsky, Stefan, Herminghaus, S., Katthän, L., Timme, M. and Vollmer, J.. (2012) Network representations of nonequilibrium steady states : cycle decompositions, symmetries, and dominant paths. Physical Review E, Vol.85 (No.4). Article no. 041133. ISSN 1539-3755

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Abstract

Non-equilibrium steady states (NESS) of Markov processes give rise to non-trivial cyclic probability fluxes. Cycle decompositions of the steady state offer an effective description of such fluxes. Here, we present an iterative cycle decomposition exhibiting a natural dynamics on the space of cycles that satisfies detailed balance. Expectation values of observables can be expressed as cycle "averages", resembling the cycle representation of expectation values in dynamical systems. We illustrate our approach in terms of an analogy to a simple model of mass transit dynamics. Symmetries are reflected in our approach by a reduction of the minimal number of cycles needed in the decomposition. These features are demonstrated by discussing a variant of an asymmetric exclusion process (TASEP). Intriguingly, a continuous change of dominant flow paths in the network results in a change of the structure of cycles as well as in discontinuous jumps in cycle weights.

Item Type:	Journal Article
Divisions:	Faculty of Science > Mathematics
Journal or Publication Title:	Physical Review E
Publisher:	American Physical Society
ISSN:	1539-3755
Date:	23 April 2012
Volume:	Vol.85
Number:	No.4
Page Range:	Article no. 041133
Identification Number:	10.1103/PhysRevE.85.041133
Status:	Peer Reviewed
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/48967

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