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tsallis_entropy.rst

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.. py:module:: dit.other.tsallis_entropy

Tsallis Entropy

The Tsallis entropy is a generalization of the Shannon (or Boltzmann-Gibbs) entropy to the case where entropy is nonextensive. It is given by:

\TE{q}{X} = \frac{1}{q - 1} \left( 1 - \sum_{x \in \mathcal{X}} p(x)^q \right)

.. ipython::

   In [1]: from dit.other import tsallis_entropy

   In [2]: from dit.example_dists import n_mod_m

   In [3]: d = n_mod_m(4, 3)

   @doctest float
   In [4]: tsallis_entropy(d, 4)
   Out[4]: 0.33331639824552489

Non-additivity

One interesting property of the Tsallis entropy is the relationship between the joint Tsallis entropy of two indpendent systems, and the Tsallis entropy of those subsystems:

\TE{q}{X, Y} = \TE{q}{X} + \TE{q}{Y} + (1-q)\TE{q}{X}\TE{q}{Y}

API

.. autofunction:: tsallis_entropy