A Gibbs-Boltzmann Approach to Conformal Prediction under Distribution Shift

Building on the foundation of standard Conformal Prediction and its known vulnerabilities to covariate shift, we formalize our Thermodynamic DRO framework. While recent methods such as Aolaritei et al. (2025) address score shift via topological metrics like the Lévy-Prokhorov distance, our approach introduces a statistical mechanics perspective. By applying a physics-inspired thermodynamic base measure directly to 1D non-conformity scores within a KL-divergence ambiguity set, we yield a smooth, closed-form partition function that expands conformal thresholds to absorb out-of-distribution errors with minimal computational overhead.