Thermally activated nonaffine rearrangements in amorphous glass: Emergence of intrinsic length scales.

We present a systematic study of temperature-driven nonaffine rearrangements in a model amorphous solid across the full thermodynamic range, from a high-temperature liquid through supercooled and subglass regimes into deeply glassy states. By subtracting the best local affine map from the particle displacements, we obtain componentwise nonaffine residuals whose exponential tails yield the characteristic length scales ξ_{NA,x} and ξ_{NA,y}. For comparison, we compute the Van Hove self-distributions G_{x}(u_{x}) and G_{y}(u_{y}) of the total particle displacement and extract the corresponding Van Hove length scale ξ_{VH}. A central result is that ξ_{VH}>ξ_{NA} for all temperatures, densities, and temporal-sampling protocols studied here, and our companion analytical derivation verifies this ordering at the model level. Notably, the particle-level nonaffine field itself reveals distinct dynamical regimes: appreciable nonaffine activity persists below the thermodynamic glass-transition temperature, indicating a mechanically active viscoelastic regime, whereas deep in the glass the field becomes strongly suppressed, signaling a mechanically locked state. The near equality of ξ_{NA,x} and ξ_{NA,y} further shows that the thermally driven nonaffine rearrangements are isotropic. Overall, the present work provides a particle-level framework for quantifying thermal nonaffinity and for distinguishing mechanically active and mechanically locked regimes in amorphous materials.