A first order Tsallis theory

We investigate first-order approximations to both (i) Tsallis’ entropy S _q and (ii) the S _q -MaxEnt solution (called q-exponential functions e _q ). We use an approximation/expansion for q very close to unity. It is shown that the functions arising from the procedure (ii) are the MaxEnt solutions to the entropy emerging from (i). Our present treatment is motivated by the fact it is FREE of the poles that, for classic quadratic Hamiltonians, appear in Tsallis’ approach, as demonstrated in A. Plastimo, M.C. Rocca, Europhys. Lett. 104, 60003 (2013)]. Additionally, we show that our treatment is compatible with extant date on the ozone layer.