Grand canonical equilibrium unifies quantum electrodynamics and statistical mechanics in wet electrolytic...

Quantum rate (QR) theory has previously shown that the charge-relaxation resistance of ferrocene redox monolayers is locked at R_q = h/2e² ≈ 12.9 kΩ at room temperature, and that electron-transfer rates are accessible from equilibrium quantum capacitance without kinetic fitting. What has remained without a first-principles thermodynamic explanation is why a room-temperature ionic bath sustains rather than destroys quantum coherence. Here, we provide that mechanism. By applying the fluctuation-dissipation theorem to the grand canonical equilibrium of an electrochemical junction, we show that minimisation of the grand canonical potential (ΔΩ = 0) defines an isoscopic condition-a thermodynamic attractor in which the classical ionic reorganisation energy (e²/C_e) and the quantum charging energy (e²/C_q) are exactly equal and opposite, compelling the electrolyte to mirror rather than oppose the quantum state. A direct experimental test of this mechanism is that the charge-relaxation resistance must be universally locked at R_q = h/2e² regardless of the solvent. We verify this prediction in ferrocene redox monolayers across three chemically distinct electrolytic environments (acetonitrile/water, acetonitrile, and dichloromethane) with a relative error of less than 7%. Furthermore, the isoscopic condition yields a parameter-free prediction of the Butler-Volmer standard rate constant, ν_μ = 8k_BT/Nh, which agrees quantitatively with an independent Laviron analysis. Together with prior QR evidence across molecular architectures, graphene, and biological films, these results establish the isoscopic condition as the thermodynamic mechanism connecting mesoscopic physics and molecular electrochemistry at room temperature.