Inspired by concepts from ergodic theory, we give a new approach to coding sequence (CDS) density estimation for the human genome. Our approach is based on the introduction and study of topological pressure: a numerical quantity assigned to any finite sequence based on an appropriate notion of "weighted information content". For human DNA sequences, each codon is assigned a suitable weight, and using a window size of approximately 60,000bp, we obtain a very strong positive correlation between CDS density and topological pressure. Inspired again by ergodic theory, we use the weightings on the codons to define a probability distribution on finite sequences, which is effective in distinguishing between coding and non-coding human DNA sequences of lengths approximately 5,000bp. The theoretical underpinning for our approach is the theory of thermodynamic formalism from the dynamical systems literature. This is joint work with David Koslicki (OSU).