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Spatially-bound objects across diverse length and energy scales arecharacterized by a binding energy. We propose that their spatial structure ismathematically encoded as information in their momentum modes and described bya measure known as configurational entropy (CE). Investigating solitonicQ-balls and stars with a polytropic equation of state $P = K{\rho}^{\gamma}$,we show that objects with large binding energy have low CE, whereas those atthe brink of instability (zero binding energy) have near maximal CE. Inparticular, we use the CE to find the critical charge allowing for classicallystable Q-balls and the Chandrasekhar limit for white dwarfs $({\gamma} = 4/3)$with an accuracy of a few percent.

Information-Entropic Stability Bound for Compact Objects: Application to Q-Balls and the Chandrasekhar Limit of Polytropes