arXiv:2509.04492v1 Announce Type: cross Abstract: Hallucinations in Large Language Model (LLM) outputs for Question Answering (QA) tasks critically undermine their real-world reliability. This paper introduces an applied methodology for robust, one-shot hallucination detection, specifically designed for scenarios with limited data access, such as interacting with black-box LLM APIs that typically expose only a few top candidate log-probabilities per token. Our approach derives uncertainty indicators directly from these readily available log-probabilities generated during non-greedy decoding. We first derive an Entropy Production Rate (EPR) metric that offers baseline performance, later augmented with supervised learning. Our learned model uses features representing the entropic contributions of the accessible top-ranked tokens within a single generated sequence, requiring no multiple query re-runs. Evaluated across diverse QA datasets and multiple LLMs, this estimator significantly improves hallucination detection over using EPR alone. Crucially, high performance is demonstrated using only the typically small set of available log-probabilities (e.g., top