The European Physical Journal B

, Volume 63, Issue 3, pp 407–415

How should complexity scale with system size?

Open Access
Topical issue dedicated to ECCS2007 - Dresden

DOI: 10.1140/epjb/e2008-00134-9

Cite this article as:
Olbrich, E., Bertschinger, N., Ay, N. et al. Eur. Phys. J. B (2008) 63: 407. doi:10.1140/epjb/e2008-00134-9


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.


89.75.-k Complex systems 89.70.+c Information theory and communication theory 
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© The Author(s) 2008

Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Max Planck Institute for Mathematics in the SciencesLeipzigGermany
  2. 2.Santa Fe InstituteSanta FeUSA

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