A possible generalization Shannon’s entropy using q-calculus

In this work, we explored two possible generalizations of Shannon’s entropy, the first one using the so-called q-algebra and the second one through the q-calculus. The expression obtained through the q-algebra cannot be used when the calculations are performed with probabilistic distributions because in several cases the results obtained are complex, while with the equation obtained with the q-calculus such problems were not detected. As a study case, we analyzed a simple chemical reaction and found that the generalization of Shannon’s entropy through Jackson’s integral can be linked to the electron correlation of the system.