If I am given a system, which I might have to describe using a generalized entropy, like the "$q$-deformed" Tsallis entropy, do I have to fit $q$ from experiment or might I know it beforehand?
How do I know the parameter $q$ and/or how can I possibly obtain the degree of non-extensitivity via experiment?
How can I measure the entropy of a part of the system, if the system is non-extensive?
After some browsing I think the answer might be related to the fact, that for $q$-deformed entropy, the most probable distribution is not the Gaussian, but seems to be the $q$-deformed Gaussian.
Then I played around a bit: [broken link].
Maybe one applies such an entropy concept if one comes across a distribution of such type, but that's only a guess. And I don't see why one would/could conclude non-extensitivity from a distribution?!