Non-linear Schroedinger equation, information entropy and gravitational quantum well

The non-linear logarithmic correction to the Schroedinger equation is constrained by the recent data on gravitational quantum well. The non-linear effects are related with information entropy and the upper bound on the phenomenological parameter, b, which determines their strength turns out to be b<2.7∗10-12eV. The uncertainty relations for the information entropy are discussed.