The Thermodynamic and Informational Constraints on Collective Aesthetic Evolution: A Non-Equilibrium Statistical Mechanics Approach to Color Desaturation in Overstimulated and Suppressed Populations

This paper introduces a mathematically rigorous framework modeling human aesthetic preference evolution as a non-equilibrium thermodynamic system governed by structural metabolic constraints. Moving beyond qualitative cultural narratives of taste, we anchor macro-aesthetic shifts to the physiological limit of the brain's approx 20W metabolic power ceiling. We resolve mathematical edge cases, notation slips, and optimization singularities from previous iterations. The boundary-constrained manifold is modeled using a standard Ginzburg-Landau potential combined with a formal soft-threshold projection operator to cleanly separate core potential minima from boundary force fields, mathematically categorized as a boundary-induced transcritical bifurcation. We introduce an analytical Phase Diagram governed by a dimensionless "Aesthetic Exhaustion Number". Crucially, we formalize the system's far-from-equilibrium behavior by deriving a generalized Fluctuation-Dissipation Theorem for Non-Equilibrium Steady States (NESS) alongside an explicit validation via Hatano-Sasa entropy production metrics. We reconcile the information-theoretic coding efficiency of color by applying Barlow's efficient coding hypothesis to low-saturation regimes. Finally, we establish an empirical operationalization strategy and cast the predictive architecture as a Physics-Informed Neural Ordinary Differential Equation (PINN-Neural ODE) utilizing a dual-regime protected log-barrier function to guarantee optimization stability and active gradient recovery against out-of-bounds states during backpropagation.