Human mutation field reveals an equilibrium-like structure with irreversible circulation

The evolution of DNA sequences can be viewed as stochastic dynamics on a high-dimensional discrete space, but it is unclear when empirical transition biases reduce to an effective energy landscape versus retain irreducible non-equilibrium circulation. Human context-dependent mutation probabilities offer a direct test: every single-nucleotide substitution in a local context has a reverse substitution, so the logarithm of the forward-to-reverse probability ratio defines an antisymmetric field-the human mutation field. We show this field has a dominant gradient component and a smaller but reproducible curl component. Using seven-base human germline substitution probabilities, we infer an effective mutational landscape with a Siamese neural network constrained to predict only energy differences. This model predicts forward-to-reverse log-ratios for held-out mutations with a correlation of about 0.93, close to both an unconstrained predictive reference (0.948) and the empirical reversible ceiling from Hodge projection (about 0.96). Although trained only on mutation probabilities, the inferred landscape largely recovers short-word genomic composition and Chargaff reverse-complement symmetry for sequences up to length four. Deviations from equilibrium structure reveal a small but detectable nonequilibrium component: a residual irreversible circulation violating the Kolmogorov cycle condition for detailed balance, reproducible across African, Asian, and European populations, and strongest in CpG-linked cycles and CpG-transition edges, consistent with methylcytosine deamination. These results give a thermodynamic decomposition of the human mutation field: most mutation bias is organized by a local equilibrium-like energy landscape aligned with genome composition, while the residual circulation points to specific directional mutational mechanisms.