The uncertainty relation expressed by means of a new entropic function

In this article we use a new entropic function, derived from an f-divergence between two probability distributions, for the construction of an alternative entropic uncertainty relation. After a brief review of some existing f-divergences, a new f-divergence and the corresponding entropic function, derived from it, is introduced and its useful characteristics are presented. This entropic function is then applied to construct an alternative uncertainty relation of two non-commuting observables in quantum physics. An explicit expression for such an uncertainty relation is found for the case of two observables which are the x- and z-components of the angular momentum of the spin-1/2 system.