A continuum support field theory with mass conservation for micro-scale structural rearrangement

We develop a mass-conserving continuum theory for micro-scale structural rearrangement in molecular systems, with proteins serving as a primary testbed. A scalar support field S(x) is constructed from topology-, geometry-, and density-based descriptors of local structural stability, and it is coupled to a continuous mass density ρ(x, t) through a physically motivated continuity equation. The resulting constitutive flux law produces a compact PDE model that preserves the total mass while allowing spatially heterogeneous accumulation and depletion of density. We establish the variational structure, conservation properties, and linear stability criteria of the theory, and we develop a finite-volume integrator suitable for densities derived from atomic coordinates. Applications to several proteins show that the Laplacian of the support field correlates strongly with experimentally accessible flexibility measures such as B-factors. The framework provides a physically interpretable and computationally efficient mesoscopic description of structural rearrangement in complex molecular environments.