Pereira, R. G.; Mukherjee, B.; Gautam, S.; D'Agnese, M.; Biswas, S.; Meeker, R.; Chakrabarti, B.

We develop a self-consistent free-energy framework in which membrane shape and osmotic pressure are determined simultaneously in a finite reservoir by minimizing bending elasticity and solute entropy. Solute conservation makes osmotic pressure a thermodynamic variable rather than an externally prescribed parameter, producing a nonlinear coupling between membrane mechanics and solvent entropy. This coupling modifies the classical stability condition for spherical vesicles: instability emerges from global free-energy competition rather than the linear Helfrich stability criterion. The resulting critical pressures differ by orders of magnitude from Helfrich predictions and agree with simulations for small and large unilamellar vesicles. The framework is relevant to cellular environments involving biomolecular condensate confinement as well as synthetic vesicles and the development of osmotic-pressure-driven encapsulation platforms.