Zero-shot detection of machine-generated text is vital for mitigating the risks of large language models (LLMs) misuse. While the state-of-the-art dual-model detectors and resampling-based detectors outperform single-model statistical detectors on unprompted continuations, they suffer a catastrophic breakdown on instruction-conditioned text in the black-box setting, where the source model is unknown. We analyze this failure and trace it to poor prompt conditioning for resampling-based methods and diminished cross-model discrepancy for dual-model detectors. Motivated by recent studies that human writing maintains a steady, uniform information flow, whereas machine-generated text exhibits sharp, localized entropy fluctuations, we propose a new metric, the Relative Peak Prominence Rate (RelPPR) to capture this structural contrast along the entropy trajectory and further leverage 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 situations. Our code is available at https://github.com/brushing-git/entropy-llm-detector.

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