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Advances in Mathematical Physics
Volume 2017, Article ID 2863614, 8 pages
Research Article

An Entropy for Groups of Intermediate Growth

Center for Research and Applications of Nonlinear Systems (CRANS), University of Patras, 26500 Patras, Greece

Correspondence should be addressed to Nikolaos Kalogeropoulos; moc.liamg@sokisyhp.sokin

Received 17 May 2017; Accepted 9 August 2017; Published 20 September 2017

Academic Editor: Andrei D. Mironov

Copyright © 2017 Nikolaos Kalogeropoulos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


One of the few accepted dynamical foundations of nonadditive (“nonextensive”) statistical mechanics is that the choice of the appropriate entropy functional describing a system with many degrees of freedom should reflect the rate of growth of its configuration or phase space volume. We present an example of a group, as a metric space, that may be used as the phase space of a system whose ergodic behavior is statistically described by the recently proposed -entropy. This entropy is a one-parameter variation of the Boltzmann/Gibbs/Shannon functional and is quite different, in form, from the power-law entropies that have been recently studied. We use the first Grigorchuk group for our purposes. We comment on the connections of the above construction with the conjectured evolution of the underlying system in phase space.