Issue Eur. Phys. J. B Volume 63, Number 3, June I 2008 Topical issue dedicated to ECCS2007 - Dresden Page(s) 407 - 415 Section Topical issue dedicated to ECCS2007 - Dresden DOI 10.1140/epjb/e2008-00134-9 Published online 02 April 2008

Eur. Phys. J. B 63, 407-415 (2008)
DOI: 10.1140/epjb/e2008-00134-9

How should complexity scale with system size?

E. Olbrich¹, N. Bertschinger¹, N. Ay^{1, 2} and J. Jost<sup>1, 2

1</sup>  Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany
²  Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

olbrich@mis.mpg.de

Received 31 August 2007 / Received in final form 17 January 2008 / Published online 2 April 2008

Abstract
We study how statistical complexity depends on the system size and how the complexity of the whole system relates to the complexity of its subsystems. We study this size dependence for two well-known complexity measures, the excess entropy of Grassberger and the neural complexity introduced by Tononi, Sporns and Edelman. We compare these results to properties of complexity measures that one might wish to impose when seeking an axiomatic characterization. It turns out that those two measures do not satisfy all those requirements, but a renormalized version of the TSE-complexity behaves reasonably well.

PACS
89.75.-k - Complex systems.
89.70.+c - Information theory and communication theory.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2008

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