Asynchronous reinforcement learning (RL) accelerates large language model (LLM) post-training by overlapping rollout generation with policy optimization, but the resulting stale, off-policy data destabilizes optimization and can cause policy collapse. Existing methods gate tokens by ratio magnitude alone, applying one threshold at every position. We show that the ratio's natural scale is set by token entropy, so deviations from mid-trajectory weight updates stay within this scale and carry genuine exploration. We further identify an overlooked low-entropy regime that breaks this scaling, where a near-zero probability amplifies train--inference mismatch into noise far beyond what the local entropy admits. A magnitude threshold admits this noise and discards the exploration. We therefore propose the Entropy-Normalized Trust Region (ENTR). Across long-horizon agentic tasks and mathematical reasoning benchmarks, ENTR outperforms existing asynchronous methods. It improves avg@1 on BrowseComp-Plus by $6.9\%$ over the strongest baseline, trains stably up to $30$ policy versions of staleness, and matches synchronous GRPO at a $2.6\times$ speedup.

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