A first order Tsallis theory

Abstract

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 theMaxEnt 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.