A key step in spatial transcriptomics is identifying genes with spatially varying expression patterns. We adopt an information theoretic perspective to this problem by equating the degree of spatial coherence with the Jensen-Shannon divergence between pairs of nearby cells and pairs of distant cells. To avoid the notoriously difficult problem of estimating information theoretic divergences, we use modern approximation techniques to implement a computationally efficient algorithm designed to scale with in situ spatial transcriptomics technologies. In addition to being highly scalable, we show that our method, which we call maximization of spatial information (Maxspin), improves accuracy across several spatial transcriptomics platforms and a variety of simulations when compared with a variety of state-of-the-art methods. To further demonstrate the method, we generated in situ spatial transcriptomics data in a renal cell carcinoma sample using the CosMx Spatial Molecular Imager and used Maxspin to reveal novel spatial patterns of tumor cell gene expression.