  Spatially-bound objects across diverse length and energy scales are
characterized by a binding energy. We propose that their spatial structure is
mathematically encoded as information in their momentum modes and described by
a measure known as configurational entropy (CE). Investigating solitonic
Q-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 at
the brink of instability (zero binding energy) have near maximal CE. In
particular, we use the CE to find the critical charge allowing for classically
stable Q-balls and the Chandrasekhar limit for white dwarfs $({\gamma} = 4/3)$
with an accuracy of a few percent.
