Felice, DomenicoDomenicoFeliceAy, NihatNihatAy2021-08-312021-08-312019-08-25Entropy 21 (9): 831 (2019-08-25)http://hdl.handle.net/11420/10197A recent canonical divergence, which is introduced on a smooth manifold M endowed with a general dualistic structure (g,∇,∇*), is considered for flat a-connections. In the classical setting, we compute such a canonical divergence on the manifold of positive measures and prove that it coincides with the classical α-divergence. In the quantum framework, the recent canonical divergence is evaluated for the quantum α-connections on the manifold of all positive definite Hermitian operators. In this case as well, we obtain that the recent canonical divergence is the quantum α-divergence.en1099-430020199MDPIhttps://creativecommons.org/licenses/by/4.0/Alpha connectionsCanonical divergenceInformation geometryKullback-Leibler divergenceQuantum relative entropyInformatikJournal Article10.15480/882.373510.3390/e2109083110.15480/882.3735Journal Article