International Journal of Theoretical Physics

, Volume 31, Issue 3, pp 525–543 | Cite as

Physical complexity and Zipf's law

  • R. Günther
  • B. Schapiro
  • P. Wagner


This article deals with a measure of the complexity of a physical system recently proposed by Schapiro and puts it into the context of other recently discussed measures of complexity. We discuss this new measure in terms of a simple Markovian evolution model, extending and specifying the model given by Schapiro, which has the advantage of being analyically tractable. We find that the proposed complexity measure leads to interesting results: there exists a kind of phase transition in this system with a vanishing value of the probabilityc of generating a new species. This phase transition is related to a specific complexity of about 3 bits. By investigating decreasingc (cN−q,N the total number of individuals), we find that the complexity per species grows monotonically withq, diverging logarithmically withN as q goes to infinity.


Phase Transition Field Theory Elementary Particle Quantum Field Theory Evolution Model 
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Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • R. Günther
    • 1
  • B. Schapiro
    • 1
  • P. Wagner
    • 1
  1. 1.Naturwissenschaftliches und Medizinisches Institut an der Universität Tübingen in ReutlingenReutlingenGermany

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