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Tsallis Entropy

The Tsallis entropy of a discrete probability distribution (p_1,...,p_n) is

S_q=k/(q-1)(1-sum_(i=1)^np_i^q),

where q is a real parameter, q!=1, and k>0 is a scale factor (Tsallis 1988). Its limit as q->1 is

lim_(q->1)S_q=-ksum_(i=1)^np_ilnp_i,

which, for k=1, is the Shannon entropy in nats.

See also

Rényi Entropy, Shannon Entropy

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References

Tsallis, C. "Possible Generalization of Boltzmann-Gibbs Statistics." J. Stat. Phys. 52, 479-487, 1988. https://doi.org/10.1007/BF01016429.

Cite this as:

Weisstein, Eric W. "Tsallis Entropy." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TsallisEntropy.html

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