Generalised definition of entropy proposed by Constantino Tsallis and defined for a random variable X to be

Sq = ∫(Pr(x))q.lnqPr(x).dx

Where lnq is the generalised logarithm

lnq(x) = (x1-q-1)/(1-q)

q is an adjustable parameter, and setting q=1 recovers the standards Shannon entropy

The Tsallis entropy has the property that it is non-extensive, in other words the Tsallis entropy of two systems considered together is not equal to the sum of their individual entropies. This form therefore can potentially describe systems with long range interactions such as self gravitating systems.

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