This work develops a causal-informational framework for quantum dynamics in finite gravitational domains. Motivated by entropy bounds and holographic reasoning, it proposes that each finite causal domain should be associated with a finite-dimensional effective Hilbert space representing the physically distinguishable states accessible within that domain. Along an observer worldline, proper time orders a sequence of causal domains and their corresponding effective state spaces. When causal accessibility grows, the effective Hilbert-space dimension may also increase. In finite dimension, such growth prevents a bijective unitary isomorphism between successive sectors. The framework therefore replaces global fixed-Hilbert-space unitarity with isometric embeddings and quantum channels between growing operational sectors, while recovering ordinary unitary quantum mechanics locally as a quasi-isomorphic approximation. The paper introduces the notion of structural leakage: a finite-scale deviation from local unitarity arising when newly accessible degrees of freedom are causally coupled to the previously accessible sector through boundary interactions. This mechanism is used to reinterpret aspects of decoherence, entropy growth, and the thermodynamic arrow of time in terms of causal-informational growth. The proposal is phenomenological and does not claim to derive quantum gravity or cosmological dynamics. Instead, it provides an operational language connecting finite information capacity, emergent local unitarity, causal-domain growth, structural leakage, and entropy increase. Possible implications for quantum information, quantum error correction, and cosmological interpretation are also discussed.