arXiv:2610.14095v1 Announce Type: cross Abstract: Importance: The search for reliable neuroimaging biomarkers of mental disorders has remained elusive despite decades of research. Why clinically consequential disorders yield weak neuroimaging separability remains unresolved. Drawing on statistical thermodynamics and the metabolic costs of neural coding, we propose that psychiatric disorders produce constrained deformations of a largely shared repertoire of brain activity patterns, limiting the class-specific information available for classification. Observations: We develop a framework linking physical resource constraints, landscape deformation, distributional separation, and attainable classification, and examine its components using human neuroimaging, synthetic data, and an exactly specified physical model. In resting-state fMRI from 1952 FOR2107 participants (823 with major depressive disorder; 1129 healthy controls), held-out energy-landscape estimates and nonlinear classifiers agreed across 13 comparisons (r = 0.996). Similar results emerged at both FOR2107 centers and in 900 SRPBS participants spanning multiple psychiatric diagnoses. In synthetic data, classification improved with distributional separation and approached the optimum. In an equilibrium three-well model, statistical energy equaled physical potential energy scaled by inverse temperature. Modest deformation redistributed state occupancy while optimal snapshot classification remained weak. A literature map found insufficiently comparable evidence to test the human metabolic constraint. Conclusions: Clinically consequential differences may arise within a largely shared neural repertoire. The thermodynamic framework connects physical deformation to classification under specified assumptions; its metabolic implementation in humans remains untested. Testing this mechanism requires joint measurements of brain activity, bodily physiology, and metabolism.