Rescaling the nonadditivity parameter in Tsallis thermostatistics

- Tsallis nonadditivity parameter rescaling transform is introduced.
- Several physical applications of the transform are discussed.
- The connection with generalized distributive rule in q-deformed calculus is pointed out.
- MaxEnt distributions of Tsallis entropy with rescaled nonadditivity parameter are calculated.

The paper introduces nonadditivity parameter transformation group induced by Tsallis entropy. We discuss simple physical applications such as systems in the contact with finite heat bath or systems with temperature fluctuations. With help of the transformation, it is possible to introduce generalized distributive rule in q-deformed algebra. We focus on MaxEnt distributions of Tsallis entropy with rescaled nonadditivity parameter under escort energy constraints. We show that each group element corresponds to one class of q-deformed distributions. Finally, we briefly discuss the application of the transformation to Jizba-Arimitsu hybrid entropy and its connection to Average Hybrid entropy.