Generalized (c, d)-Entropy and Aging Random Walks

@article{Hanel2013GeneralizedD,
  title={Generalized (c, d)-Entropy and Aging Random Walks},
  author={Rudolf Hanel and Stefan Thurner},
  journal={Entropy},
  year={2013},
  volume={15},
  pages={5324-5337}
}
Complex systems are often inherently non-ergodic and non-Markovian and Shannon entropy loses its applicability. Accelerating, path-dependent and aging random walks offer an intuitive picture for non-ergodic and non-Markovian systems. It was shown that the entropy of non-ergodic systems can still be derived from three of the Shannon–Khinchin axioms and by violating the fourth, the so-called composition axiom. The corresponding entropy is of the form Sc,d ~ ∑iΓ(1 + d, 1 − cln pi) and depends on… 

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