Dynamic novel view synthesis (NVS) aims to render time-varying scenes from arbitrary viewpoints, balancing rendering quality and computational efficiency. While recent 4D Gaussian Splatting approaches offer promising real-time performance, they fundamentally overlook critical interdependence between Gaussians by modeling deformations independently. Our information-theoretic analysis reveals substantial mutual information across the Gaussian field, manifesting as appearance-preserving radiance coherence and motion-consistent deformation propagation. This finding establishes that rendering quality emerges from coordinated transformation rather than independent processing. We propose Correlation-aware Dynamic Gaussian Splatting (CaDGS) with our novel Gaussian Correlation Tensor Projection (GCTP) method, which efficiently transforms the complex O(n3) mutual information tensor into a dual-channel O(n2) spatial matrix, preserving the critical topological structure of Gaussian interactions. Combined with our Spatio-Temporal Deformation Consistency (STDC) learning, which enforces volumetric coherence through tensor-guided regularization across multiple scales, CaDGS prevents geometric distortions and texture inconsistencies common in previous approaches. Experimental results demonstrate state-of-the-art performance, achieving 32.4 PSNR on the Neu3D dataset with fewer Gaussians while maintaining rendering speeds of 323 FPS at 1353 × 1014 resolution.