### Abstract

We present an extension of a novel method for understanding complex systems, which has been applied to non-equilibrium systems both in and out of detailed balance. For the non-detailed balance case, in which non-zero currents are a principal indicator of complexity, there has been an incomplete understanding of the distance function in the observable representation embedding. To deal with this we construct a new transition matrix by accounting for this current and compute the eigenvalues and eigenvectors. From these, we define a metric whose distance provides a useful measure of the relation among variables. Use of this method provides insights into long-range correlation, and chaotic properties. As an example we show that these distances can be used to control chaos in a simple dynamical system.

Original language | English |
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Pages (from-to) | 1810-1813 |

Number of pages | 4 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 377 |

Issue number | 31-33 |

Early online date | 22 May 2013 |

DOIs | |

Publication status | Published - 30 Oct 2013 |

Externally published | Yes |

### Keywords

- Chaos
- Complex systems
- Detailed balance
- Irreversible
- Non-equilibrium

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*377*(31-33), 1810-1813. https://doi.org/10.1016/j.physleta.2013.05.036