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Order in a multidimensional system.

B Roy Frieden1, Robert A Gatenby

  • 1College of Optics, University of Arizona, Tucson, Arizona 85721, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

A new order measure (R) is proportional to Fisher information (I) in convex systems. This finding establishes an arrow of time and offers a universal measure of complexity, applicable from physics to cell biology.

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Area of Science:

  • Theoretical Physics
  • Information Theory
  • Complexity Science

Background:

  • Fisher Information (I) quantifies data in statistical models.
  • Existing measures of order lack universal applicability and objectivity.
  • Understanding system complexity is crucial across scientific disciplines.

Purpose of the Study:

  • To introduce a new, objective measure of order (R) for K-dimensional systems.
  • To establish the relationship between this new order measure and Fisher Information (I).
  • To explore the implications of this relationship for defining an arrow of time and quantifying complexity.

Main Methods:

  • Derivation of the order measure (R) based on its decrease under coarse-graining.
  • Establishing proportionality between order (R) and Fisher Information (I).
  • Analyzing invariance properties (unitless, magnification) and monotonic contraction.

Main Results:

  • Order (R) is proportional to Fisher Information (I) in convex systems, with a constant related to system geometry.
  • The order measure (R) is unitless and invariant to uniform magnification, enabling objective comparisons.
  • Monotonic contraction of R and I implies an arrow of time and suggests they are entropies.

Conclusions:

  • The new order measure (R) provides a universal and objective quantification of system complexity.
  • The relationship between R and I offers a data-independent derivation for non-participatory phenomena.
  • Application to cell membranes demonstrates R's utility in biological contexts, linking hydrocarbon chains to cellular structures.