Connectivity Maintenance Cost: A Thermodynamic Threshold Model for the Failure Sequence of Sustained Biological Networks, with Application to Neurodegeneration

Preprint. This manuscript is simultaneously under editorial consideration at BioSystems (Elsevier). Corresponding author: [email protected] Living systems are dissipative structures: they persist only while energy flows sustain their internal order. This paper applies that principle at a level not previously formalised — the functional coupling between elements of a biological network. It introduces Connectivity Maintenance Cost (CMC), a threshold model in which coupling between regions of the brain’s connectome requires a minimum continuous energetic expenditure, and in which crossing below this threshold, not element death, is the primary failure event. Network neuroscience explains the connectome’s topology as a trade-off between wiring cost and topological efficiency, but this economic account is a theory of formation with no model of failure; CMC supplies the missing failure term. Five testable propositions are derived from an established thermodynamic and physiological lineage and operationalised using existing imaging modalities. The framework predicts that the clinical sequence of cognitive decline reflects the CMC gradient of the connectome, and that cortical hubs of the default mode network fail first because they carry the highest continuous connectivity cost — a prediction consistent with existing evidence on hub vulnerability to amyloid deposition and with the persistence of clinical decline despite amyloid clearance. Falsification conditions are specified, along with a proposed re-analysis of existing multimodal datasets requiring no new data collection. The framework is positioned relative to wiring-cost economy models of network formation and to the two-hit vascular hypothesis of neurodegeneration, which it extends with a quantitative ordering principle and a candidate mechanism linking hub connectivity to regional vulnerability.