When do generalized entropies apply? How phase space volume determines entropy

@article{Hanel2011WhenDG,
  title={When do generalized entropies apply? How phase space volume determines entropy},
  author={Rudolf Hanel and Stefan Thurner},
  journal={EPL},
  year={2011},
  volume={96},
  pages={50003}
}
We show how the dependence of phase space volume Ω(N) on system size N uniquely determines the extensive entropy of a classical system. We give a concise criterion when this entropy is not of Boltzmann-Gibbs type but has to assume a generalized (non-additive) form. We show that generalized entropies can only exist when the dynamically (statistically) relevant fraction of degrees of freedom in the system vanishes in the thermodynamic limit. These are systems where the bulk of the degrees of… 

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