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 - 12 eV . The uncertainty relations for the information entropy are discussed.