Relative Renyi entropy and fidelity susceptibility

It is shown that there is a linear relation between the relative Renyi entropy and the density functional fidelity susceptibility. The derivative of the relative Renyi entropy with respect to the Renyi parameter a is also proportional to the density functional fidelity susceptibility. The benefit of these relations is illustrated for the Dicke model (considering a numerical study and a variational analytical approximation). These relations are useful to detect the second-order QPT in this model. Copyright (C) EPLA, 2015.