Large reasoning models have demonstrated remarkable performance on complex reasoning tasks, yet the excessive length of their chain-of-thought outputs remains a major practical bottleneck due to high computation cost and poor deployability. Existing compression methods have achieved partial success but overlook a crucial phenomenon in the training process -- the entropy conflict. During compression training, entropy decreases, leading to shorter reasoning but limited exploration, while accuracy-oriented objectives increase entropy, lengthening reasoning chains. This can cause the model to get stuck in a local dilemma. Our analysis further reveals the origin of the entropy conflict: many high-entropy tokens are logical connectors that receive larger gradients and are encouraged under the performance objective, while the compression objective simultaneously penalizes these potentially redundant connectors. This opposing pressure creates a direct source of entropy conflict. To address these issues, we adopt an entropy-guided training framework. As entropy descends, the model is guided toward efficient reasoning by encouraging concise thought steps; as entropy rises, exploration is reinforced under the compact reasoning mode to improve robustness. Experiments on six mathematical benchmarks show that our method compresses reasoning length to 20% of the original while maintaining or even surpassing baseline accuracy. Code and models will be released publicly.