Beyond Integration: Neural Dimensionality and the Landau-Ginzburg Physics of Awareness

Two-dimensional accounts of consciousness that distinguish global integration from functional diversity are empirically supported [1,2] but lack a formal phase-structure: they do not specify the nature of the transition between the two regimes, the order parameter that governs it, or the quantitative predictions that follow. We provide this structure. We propose that the dimensionality of the neural correlation structure, operationalised as the Participation Ratio of the covariance eigenspectrum, constitutes a second, independent order parameter D that governs a phase transition distinct from global integration {Phi}. Formalised through a Landau-Ginzburg free energy functional F[{Phi}, D], this transition defines a Redundant Integrated State {Delta} (high {Phi}, low D) in which globally integrated mental function is present but phenomenal experience is absent, a thermodynamic phase, not a point on a continuum. The framework generates three falsifiable predictions absent from prior work: (i) a power-law scaling D* [~] |{Phi} - {Phi}_c|^{nu} with measurable critical exponent{nu} ; (ii) a diverging susceptibility {chi}_D = {partial}D/{partial}{Phi} at the consciousness threshold, quantifiable from perturbational EEG; (iii) an explicit dissociation between MCS and VS patients in the ({Phi}, D) space, with MCS predicted to occupy state {Delta}. These predictions are directly testable with existing methodology and are not generated by any current theory of consciousness.