Network representations of nonequilibrium steady states: Cycle decompositions, symmetries, and dominant paths.
Phys Rev E Stat Nonlin Soft Matter Phys
; 85(4 Pt 1): 041133, 2012 Apr.
Article
en En
| MEDLINE
| ID: mdl-22680444
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.
Buscar en Google
Colección:
01-internacional
Banco de datos:
MEDLINE
Asunto principal:
Reología
/
Cadenas de Markov
/
Modelos Teóricos
Tipo de estudio:
Health_economic_evaluation
Idioma:
En
Revista:
Phys Rev E Stat Nonlin Soft Matter Phys
Asunto de la revista:
BIOFISICA
/
FISIOLOGIA
Año:
2012
Tipo del documento:
Article
País de afiliación:
Alemania