SUM RULE FOR MULTISCALE REPRESENTATIONS OF KINEMATICALLY DESCRIBED SYSTEMS

Yaneer Bar-Yam ()
Additional contact information
Yaneer Bar-Yam: New England Complex Systems Institute, 24 Mt. Auburn St., Cambridge, MA 02138, USA

Advances in Complex Systems (ACS), 2002, vol. 05, issue 04, 409-431

Abstract: We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum rule can be related to the moment of inertia and the kinetic energy (times a characteristic time squared). Thus, two nonequilibrium systems that have the same kinetic energy and moment of inertia can, when compared to each other, have different scales of behavior, but if one of them has larger scales of behavior than the other, it must compensate by also having smaller scales of behavior. In the context of coherence or correlation, the larger scale of behavior corresponds to the collective motion, while the smaller scales of behavior correspond to therelativemotion of correlated particles. For longer duration trajectories, the sum rule includes the full effective moment of inertia of the system in space-time with respect to an external frame of reference, providing the possibility of relating the class of systems that can exist in the same space-time domain.

Keywords: Complex systems; multiscale representations; entropy; complexity; scale; collective behaviors; nonequilibrium thermodynamics (search for similar items in EconPapers)
Date: 2002
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219525902000638
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:acsxxx:v:05:y:2002:i:04:n:s0219525902000638

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219525902000638

Access Statistics for this article

Advances in Complex Systems (ACS) is currently edited by Frank Schweitzer

More articles in Advances in Complex Systems (ACS) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().