Spatiotemporal Topological Order as a Dissipative Structure: A Field-Theoretic Model of Metabolic Failure in Alzheimer’s Disease

Abstract

Binggong Chang

Three decades of research on the amyloid-β cascade hypothesis have yielded limited translational success, and a growing body of evidence indicates that metabolic and functional decline in Alzheimer's disease (AD) precedes structural pathology by years to decades. Here we propose that AD is fundamentally a failure of dissipative self-organization rather than a disease of molecular lesion accumulation. Drawing on non-equilibrium thermodynamics, we model the brain's large-scale functional integration as a Spatiotemporal Topological Order (STTO)—a hierarchical, four-level field structure (molecular, synaptic, mesoscopic, and global network scales) that is actively sustained, rather than passively encoded, by continuous metabolic energy flux. We derive a coupled field-theoretic formalism in which each level is governed by a Klein-Gordon-Langevin equation, and show, via adiabatic elimination of fast variables, that the global network mode obeys an effective Ginzburg-Landau dynamic with a dimensionless control parameter η (the ratio of biological to critical metabolic power). When η falls below unity, the system undergoes a continuous phase transition characterized by critical slowing down, divergent correlation length, and network fragmentation—providing a mechanistic account of the default mode network disintegration observed in AD. Within this framework, amyloid-β and tau aggregates are reinterpreted as thermodynamically inevitable "entropy crystals" precipitated by decoherence, rather than primary pathogenic agents. The model generates three falsifiable predictions—a spectral scaling transition in EEG/MEG (1/f-to-white noise), an ascending "anti-causal" rebound in network metrics following molecular-level intervention, and a discrete critical transition in the metabolism–cognition relationship—each mapped onto concrete validation protocols using existing longitudinal FDG-PET, resting-state fMRI, and EEG datasets (ADNI, UK Biobank, OASIS-3). We further outline a staged, biomarker-guided therapeutic framework prioritizing restoration of metabolic and cross-scale coupling over amyloid clearance. This hypothesis offers a unifying, testable explanation for why metabolic failure—not molecular pathology—may be the primary driver of cognitive collapse in Alzheimer's disease.

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