Zero-shot detection of machine‑generated text is essential for mitigating misuse of large language models (LLMs). State‑of‑the‑art dual‑model detectors and resampling‑based detectors outperform single‑model statistical methods on unprompted continuations, yet they catastrophically fail on instruction‑conditioned text when the source model is unknown (black‑box setting).\ \ We trace this failure to two factors: resampling methods suffer from poor prompt conditioning, and dual‑model detectors experience reduced cross‑model discrepancy.\ \ Recent studies show that human writing maintains a steady, uniform information flow, whereas machine‑generated text exhibits sharp, localized entropy fluctuations. Inspired by this, we introduce the Relative Peak Prominence Rate (RelPPR) to capture the structural contrast along the entropy trajectory and use it as a signal for LLM‑generated text detection.\ \ Extensive evaluations across diverse model families and datasets demonstrate that RelPPR achieves state‑of‑the‑art black‑box detection performance and remains the most reliable detector under various practical conditions.\ \ The implementation is publicly available at https://github.com/brushing-git/entropy-llm-detector\ \ Review