@GSPfunction3]. By this we mean that the occurrence of nonclassicality via each of the above indicators leads to the non-positivity of the corresponding $P$-function. But, since deriving this function is usually a hard task (if not impossible), this paper is allocated to study the above nonclassicality indicators which are really independent of each other and of the previously considered properties in [@usJOSA], too. To make our motivations of this presentation more clear, we give a few words on the notability of the considered physical (nonclassical) criteria. Starting with the number-phase entropic uncertainty relation, it should be mentioned that, studying the quantum phase properties leads to the investigating the variation of the phase relation between the photons of the field. Moreover, it has been shown that for the single-mode JCM the evolution of the phase variance, as well as the phase distribution can carry certain information on the collapse-revival phenomenon of the corresponding atomic inversion [@dung]. Altogether, to achieve this purpose, it ought to be mentioned that, for discussing the dynamical behaviour of the phase properties, we will suitably extend the Pegg-Barnett formalism [@pb] to be utilizable for our considered model. Regarding CSI, it may be noted that, the violation of 