Dynamically changing interface as a model of measurement in complex systems

Yukio Pegio Gunji, Shin'ichi Toyoda

Research output: Contribution to journalArticle

22 Citations (Scopus)

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/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.

Original languageEnglish
Pages (from-to)27-54
Number of pages28
JournalPhysica D: Nonlinear Phenomena
Volume101
Issue number1-2
DOIs
Publication statusPublished - 1997 Jan 1

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ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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