Title: Protein Conditioned Free-Energy Density via Unbalanced Solutions to Constraint Satisfaction Problems

Abstract: This study demonstrates that calculating the log-partition function, or free-energy, for conditioned inhomogeneous Curie–Weiss spin Hamiltonians can be reduced to computing an unbalanced $2 \to 1$ norm. To address this, we have developed a polynomial-time semi-definite programming (SDP) algorithm and established a proof regarding the lower bound of the unbalance attained. When applied to the protein Ubiquitin, our approach begins with a known crystal structure to navigate the free-energy landscape, uncovering alternative backbone conformations. This method successfully pinpoints the protein’s flexible regions while maintaining its native secondary structure.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC