A measure on a space is invariant if it is preserved by the action of each element of the group. A measure is stationary if it is equal to the average, according to some probability measure, of its translates by group elements. The Furstenberg entropy is an invariant of stationary systems that measures the lack of invariance. In particular it vanishes for invariant measures. The aim of the talk is to give a description of all possible values taken by the Furstenberg entropy of stationary actions of SL(d,R) endowed with a reasonable probability measure. It is a joint work with Tianyi Zheng.