Applications of information theory to compact objects: configurational entropy as a stability criterion

M. Gleiser and N. Jiang [Phys. Rev. D 92, 044046, 2015] established that, within the simple Fermi gas model and self-gravitating complex scalar field configurations, the stability regions of neutron stars—determined using conventional perturbation techniques—align with the critical points of the configurational entropy, with deviations of only a few percent. Extending their work, we employ a range of realistic equations of state, suitable to describe neutron stars, quark stars, and hybrid stars (twin stars), to explore the potential correlation. Our findings indicate that, at least quantitatively, the proposed stability prediction lacks universal validity for neutron and quark stars. Furthermore, to enrich our analysis, we compute the configurational entropy for bosonic and fermionic systems (interacting boson and Fermi gases), revealing a strong correlation between the stability points predicted by configurational entropy and those obtained through traditional methods, with a slight dependence on interaction strength. In conclusion, configurational entropy can be a valuable tool for studying compact object stability, though its predictive accuracy depends on the specific equation of state.