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The Csisz\'ar f-divergence, which is a class of information distances, isknown to offer a useful tool for analysing the classical counterpart of thecloning operations that are quantum mechanically impossible for the factorizedand marginality classical probability distributions under Liouville dynamics.We show that a class of information distances that does not belong to thisdivergence class also allows for the formulation of a classical analogue of thequantum no-cloning theorem. We address a family of nonlinear Liouville-likeequations, and generic distances, to obtain constraints on the correspondingfunctional forms, associated with the formulation of classical analogue of theno-cloning principle.

Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence