The analogy to heat diffusion has enhanced our understanding of information flow in graphs and inspired the development of Graph Neural Networks (GNNs). However, most diffusion-based GNNs emulate passive heat diffusion, which still suffers from over-smoothing and limits their ability to capture global graph information. Inspired by the heat death of the universe, which posits that energy distribution becomes uniform over time in a closed system, we recognize that, without external input, node representations in a graph converge to identical feature vectors as diffusion progresses. To address this issue, we propose the Active Diffusion-based Graph Neural Network (ADGNN). ADGNN achieves active diffusion by integrating multiple external information sources that dynamically influence the diffusion process, effectively overcoming the over-smoothing problem. Furthermore, our approach realizes true infinite diffusion by directly calculating the closed-form solution of the active diffusion iterative formula. This allows nodes to preserve their unique characteristics while efficiently gaining comprehensive insights into the graph's global structure. We evaluate ADGNN against several state-of-the-art GNN models across various graph tasks. The results demonstrate that ADGNN significantly improves both accuracy and efficiency, highlighting its effectiveness in capturing global graph information and maintaining node distinctiveness.