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  Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths

Altaner, B., Grosskinsky, S., Herminghaus, S., Katthän, L., Timme, M., & Vollmer, J. (2012). Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths. Physical Review E, 85: 041133. doi:10.1103/PhysRevE.85.041133.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0029-10E9-0 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-002B-2708-4
Genre: Journal Article

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 Creators:
Altaner, Bernhard1, Author              
Grosskinsky, Stefan, Author
Herminghaus, Stephan2, Author              
Katthän, L., Author
Timme, Marc3, Author              
Vollmer, Jürgen1, Author              
Affiliations:
1Group Principles of Self Organisation, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063312              
2Group Granular matter and irreversibility, Department of Dynamics of Complex Fluids, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063306              
3Max Planck Research Group Network Dynamics, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society, ou_2063295              

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 Abstract: Nonequilibrium steady states of Markov processes give rise to nontrivial 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. 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.

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Language(s): eng - English
 Dates: 2012-04-23
 Publication Status: Published in print
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 Table of Contents: -
 Rev. Method: Peer
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Title: Physical Review E
  Alternative Title : Phys. Rev. E
Source Genre: Journal
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Pages: 8 Volume / Issue: 85 Sequence Number: 041133 Start / End Page: - Identifier: -