Entropy-Aware Memory Systems for Continual Learning: Balancing Neuroplasticity and Stability Under Stochastic Workloads

Continual learning systems are increasingly limited by memory behavior rather than arithmetic throughput: the same memory substrate must support stable recall and adaptive updates while respecting strict latency and energy constraints. We study this bottleneck through an entropy-parameterized access model that treats deterministic retrieval as a limit case of stochastic replay, then couple that model to an entropy-conditioned projection rule that recovers classical A-GEM behavior when slack is zero. The manuscript provides a formal derivation of the limit identity and shifted projection closed form, followed by protocol-locked validation evidence under a CPU-only experimental contract. Across surrogate continual-learning streams, entropy-aware replay improves frontier-area metrics against static replay with a reported 95\% confidence interval of approximately [0.0533,0.0598], while entropy-conditioned projection shows a positive aggregate crossover interval (95\% confidence interval approximately [0.028,0.194]) relative to fixed A-GEM in validated operating regions. Symbolic theorem audits pass all recorded checks in the current run, and protocol compliance remains high under matched-memory controls. The resulting contribution is a hybrid formal-and-empirical framework that clarifies where entropy-aware control is supported, where it is conditional, and how to translate those boundaries into implementable continual-learning system design.