Temporal networks are widely used as abstract graph representations for real-world dynamic systems. Indeed, recognizing the network evolution states is crucial in understanding and analyzing temporal networks. For instance, social networks will generate the clustering and formation of tightly-knit groups or communities over time, relying on the triadic closure theory. However, the existing methods often struggle to account for the time-varying nature of these network structures, hindering their performance when applied to networks with complex evolution states. To mitigate this problem, we propose a novel framework called ESSEN, an Evolution StateS awarE Network, to measure temporal network evolution using von Neumann entropy and thermodynamic temperature. The developed framework utilizes a von Neumann entropy aware attention mechanism and network evolution state contrastive learning in the graph encoding. In addition, it employs a unique decoder the so-called Mixture of Thermodynamic Experts (MoTE) for decoding. ESSEN extracts local and global network evolution information using thermodynamic features and adaptively recognizes the network evolution states. Moreover, the proposed method is evaluated on link prediction tasks under both transductive and inductive settings, with the corresponding results demonstrating its effectiveness compared to various state-of-the-art baselines.