Reinforcement Learning with Verifiable Rewards (RLVR) serves as a cornerstone technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, its training is often plagued by \emph{entropy collapse}, a rapid decline in policy entropy that limits exploration and undermines training effectiveness. While recent works attempt to mitigate this issue via several heuristic entropy interventions, the underlying mechanisms remain poorly understood. In this work, we conduct comprehensive theoretical and empirical analyses of entropy dynamics in RLVR, offering two main insights: (1) We derive a tight analytical approximation for token-level entropy change at each update step, revealing four governing factors and providing a unified theoretical framework to explain how existing methods influence entropy; (2) We reveal a fundamental limitation of recent approaches: they rely on heuristic adjustments to one or two of these factors, leaving other relevant factors unconsidered, thus inherently limiting their effectiveness. Motivated by these findings, we propose STEER, a principled entropy-modulation method that adaptively reweights tokens based on theoretically-estimated entropy variations. Extensive experiments across six mathematical reasoning and three coding benchmarks demonstrate that STEER effectively mitigates entropy collapse and consistently outperforms state-of-the-art baselines.

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