Learning task-relevant state representations is crucial to solving the problem of scene generalization in visual deep reinforcement learning. Prior work typically establishes a self-supervised auxiliary learner, introducing elements (e.g., rewards and actions) to extract task-relevant state information from observations through behavioral similarity metrics. However, the methods often ignore the inherent relationships between the elements (e.g., dynamics relationships) that are essential for learning accurate representations, and they are also limited to single-step metrics, which impedes the discrimination of short-term similar task/behavior information in long-term dynamics transitions. To solve the issues, we propose an intrinsic dynamic characteristics-driven sequence representation learning method (DSR) over a common DRL frame. Concretely, inspired by the fact of state transition in the underlying system, it constrains the optimization of the encoder via modeling the dynamics equations related to the state transition, which prompts the latent encoding information to satisfy the state transition process and thereby distinguishes state space and noise space. Further, to refine the ability of encoding similar tasks based on dynamics constraints, DSR also sequentially models inherent dynamics equation relationships from the perspective of sequence elements' frequency domain and multi-step prediction. Finally, experimental results show that DSR has achieved a significant performance boost in the Distracting DMControl Benchmark, with an average of 78.9% over the backbone baseline. Further results indicate that it also achieves the best performance in real-world autonomous driving tasks in the CARLA simulator. Moreover, the qualitative analysis results of t-SNE visualization validate that our method possesses superior representation ability on visual tasks.