Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Network representations of non-equilibrium steady states: Cycle
  decompositions, symmetries and dominant paths   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.

15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph