### Abstract

We propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system. We call this approach hyper-dilation and cover it under the label of measurement-oriented physics (MOP) as compared with state-oriented physics (SOP). The essential difference between the two concerns the concepts of state to which they refer. MOP deals with two different concepts of state; non measured states with infinite precision and measured states with finite precision. The measurement process is expressed as a dynamically changing interface between them. SOP deals with one single concept of state and does not comprise a corresponding distinction. We show fundamental differences between MOP and SOP with respect to the noise characteristics of complex systems around critical states. MOP can give rise to exact and universal 1/f noise, while SOP shows 1/f^{α} noise with α ≠ 1 in general. In MOP a self-similar return map can be degenerate with a Cantor set, rendering a solution for a basic measurement paradox. The significance of this degeneracy as a model for emergent properties is discussed.

Original language | English |
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Pages (from-to) | 27-54 |

Number of pages | 28 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 101 |

Issue number | 1-2 |

Publication status | Published - 1997 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

*Physica D: Nonlinear Phenomena*,

*101*(1-2), 27-54.

**Dynamically changing interface as a model of measurement in complex systems.** / Gunji, Yukio; Toyoda, Shin'ichi.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 101, no. 1-2, pp. 27-54.

}

TY - JOUR

T1 - Dynamically changing interface as a model of measurement in complex systems

AU - Gunji, Yukio

AU - Toyoda, Shin'ichi

PY - 1997

Y1 - 1997

N2 - We propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system. We call this approach hyper-dilation and cover it under the label of measurement-oriented physics (MOP) as compared with state-oriented physics (SOP). The essential difference between the two concerns the concepts of state to which they refer. MOP deals with two different concepts of state; non measured states with infinite precision and measured states with finite precision. The measurement process is expressed as a dynamically changing interface between them. SOP deals with one single concept of state and does not comprise a corresponding distinction. We show fundamental differences between MOP and SOP with respect to the noise characteristics of complex systems around critical states. MOP can give rise to exact and universal 1/f noise, while SOP shows 1/fα noise with α ≠ 1 in general. In MOP a self-similar return map can be degenerate with a Cantor set, rendering a solution for a basic measurement paradox. The significance of this degeneracy as a model for emergent properties is discussed.

AB - We propose and sketch a novel approach toward the study of complex systems by considering a basic type of measurement problem hidden in any system. We call this approach hyper-dilation and cover it under the label of measurement-oriented physics (MOP) as compared with state-oriented physics (SOP). The essential difference between the two concerns the concepts of state to which they refer. MOP deals with two different concepts of state; non measured states with infinite precision and measured states with finite precision. The measurement process is expressed as a dynamically changing interface between them. SOP deals with one single concept of state and does not comprise a corresponding distinction. We show fundamental differences between MOP and SOP with respect to the noise characteristics of complex systems around critical states. MOP can give rise to exact and universal 1/f noise, while SOP shows 1/fα noise with α ≠ 1 in general. In MOP a self-similar return map can be degenerate with a Cantor set, rendering a solution for a basic measurement paradox. The significance of this degeneracy as a model for emergent properties is discussed.

UR - http://www.scopus.com/inward/record.url?scp=0031079104&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031079104&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031079104

VL - 101

SP - 27

EP - 54

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -