Abstract <p>The link between the phase-space Fisher information and Rényi entropy is explored in the thermodynamic scheme of density functional theory. The momentum-space part of the phase-space Rényi entropy can be expressed with the phase-space Fisher information in the case of constant temperature. Both measures can be given by the kinetic energy. Moreover, in Coulomb systems they can be related to the total energy as well as energy differences, and excitation energies can also be provided by these information measures.</p> Graphical Abstract <p>Link between the phase-space Fisher information and R´enyi entropy is established in the thermodynamic scheme of density functional theory. The position and momentum parts of the Rényi entropy are investigated in case of constant temperature. </p>