Tsallis entropy and other generalizations

Questions:

1. 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?

2. How do I know the parameter $$q$$ and/or how can I possibly obtain the degree of non-extensitivity via experiment?

3. How can I measure the entropy of a part of the system, if the system is non-extensive?

Edit

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?!

• Can you give one example? I am struggling to find a single case which is described by this thing. Oct 10 '11 at 6:04
• The kappa velocity distribution function is related to the Tsallis q-distribution and has been heavily researched in space plasma physics. Mar 7 '16 at 18:00
• There are some papers that derive a value for $q$ in some model or another. If you're interested in the applications of Tsallis $q$-statistics to a particular system, it's worth reading the existing research on it to see whether any such derivation exists. Of course, even if it does empirical data can test that.
– J.G.
May 15 '18 at 20:44