The Gentile statistics interpolates between the standard bosonic and fermionic statistics, allowing an intermediate maximum state occupation 1< M < ∞. A generalization of this statistics having the Gibbs factor phenomenologically substituted with the nonadditive Tsallis q-exponential is analyzed. Depending on the values of the statistics parameter q, peculiarities of the thermodynamic functions are observed: for q > 1, a finite (nonzero) minimum temperature arises in the model, while for q < 1, the specific heat does not tend to zero at T → 0. These results are consistent with previously reported for a similar generalization of the fermionic statistics [A. Rovenchak and B. Sobko, Physica A 534, 122098 (2019)]. Their relevance for modeling phenomena in real physical systems is briefly outlined.
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