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In this paper, a new exponential and logarithm related to the non-extensivestatistical physics is proposed by using the q-sum and q-product which satisfythe distributivity. And we discuss the q-mapping from an ordinary probabilityto q-probability. The q-entropy defined by the idea of q-probability is shownto be q-additive.

New exponential, logarithm and q-probability in the non-extensive statistical physics