Configurational entropy and stability conditions of fermion and boson stars

In a remarkable study by M. Gleiser and N. Jiang (Phys. Rev. D {\bf 92}, 044046, 2015), the authors demonstrated that the stability regions of neutron stars, within the framework of the simple Fermi gas model, and self-gravitating configurations of complex scalar field (boson stars) with various self couplings, obtained through traditional perturbation methods, correlates with critical points of the configurational entropy with an accuracy of a few percent. Recently, P. Koliogiannis \textit{et al.} (Phys. Rev. D {\bf 107}, 044069 2023) found that while the minimization of the configurational entropy generally anticipates qualitatively the stability point for neutron stars and quark stars, this approach lacks universal validity. In this work, we aim to further elucidate this issue by seeking to reconcile these seemingly contradictory findings. Specifically, we calculate the configurational entropy of bosonic and fermionic systems, described by interacting Fermi and Boson gases, respectively, that form compact objects stabilized by gravity. We investigate whether the minimization of configurational entropy coincides with the stability point of the corresponding compact objects. Our results indicate a strong correlation between the stability points predicted by configurational entropy and those obtained through traditional methods, with the accuracy of this correlation showing a slight dependence on the interaction strength. Consequently, the stability of compact objects, composed of components obeying Fermi or Boson statistics, can alternatively be assessed using the concept of configurational entropy.