Abstract:  We apply a unified framework called configurational entropy (CE) to address the stability issues of various physical systems. The CE is a shannon-like shape complexity measure constructed from the Fourier transform. We first obtain bounds on the stability regions of self-gravitating astrophysical objects including Newtonian polytropes, neutron stars with an Oppenheimer-Volkoff equation of state and self-gravitating complex scalar field (boson stars) with accuracy of a few percent. We then show that CE can serve as a predictor of spontaneous decay rates for the hydrogen atom. Finally, we demonstrate that CE also tracks the trend of false vacuum decay rates.