The vacuum catastrophe—the approximately -fold discrepancy between the vacuum energy density predicted by quantum field theory and the observed cosmological constant—remains the most severe mismatch between theory and experiment in modern physics. Existing approaches invoke supersymmetry, anthropic selection in vast vacuum landscapes, or modified gravity, yet none derive the observed value dynamically without fine tuning or untestable assumptions. Here we propose a candidate thermodynamic resolution: the effective cosmological constant is exponentially suppressed by entropy-paid branch selection in an open quantum cosmological system. Treating vacuum fluctuations as a noise reservoir rather than a direct gravitational source, we show that irreversible selection of classical histories absorbs vacuum energy into non-observable exhaust channels. The resulting effective cosmological constant is where is the dimensionless entropy cost associated with branch stabilization. A conservative estimate , motivated by vacuum mode hierarchies, yields without parameter tuning. The framework predicts mildly evolving dark energy, with , consistent with recent large-scale-structure indications of weakening cosmic acceleration. Distinct, falsifiable signatures—including correlated CMB spectral deviations and horizon entropy bounds—differentiate this mechanism from landscape or modified-gravity models. While motivated by Coherence-Selection Interface Theory, the derivation relies only on open-system quantum mechanics and thermodynamics. If validated, entropy-paid branch selection provides a candidate physical resolution of the vacuum catastrophe. Keywords: vacuum catastrophe, cosmological constant problem, dark energy, entropy production, quantum cosmology, open quantum systems, decoherence, thermodynamic irreversibility, multiverse selection, information erasure