Configurational entropy as a probe of the stability condition of compact objects

We systematically extend the statement that the configurational entropy provides an alternative approach to studying gravitational stability of compact objects, carried out in the previous work of M. Gleiser and N. Jiang, Phys. Rev. D {\bf 92}, 044046 (2015). Inspired by that paper, we try to answer the crucial question: Is there any one-to-one correspondence between the minimum of the configurational entropy and the stability point for each realistic equation of state? In view of the above question, we focus on neutron stars, quark stars, as well as on the third family of compact stars (hybrid stars), where a possible phase transition may lead to the existence of twin stars (stars with equal mass but different radius). In each case, we use a large set of equations of state investigating the possibility to find correlations between the stability region obtained from the traditional perturbation methods to the one obtained by the minimum of configurational entropy. We found that the suggested prediction of the stability by the minimization of the configurational entropy, concerning neutron stars and quark stars, does not have, at least quantitatively, universal validity. However, in several cases it qualitatively predicts the existence of the stability point. In conclusion, the configurational entropy, can be considered as an additional tool which enters into the quiver for studying the stability of compact objects such as for example neutron and quark stars, but taking into account that the accuracy of the predictions depends on the specific character of each equation of state.