This is defined by the equation: \[U^{\ddagger } = -R\ T\ (\frac{\partial (\ln I_{0})}{\partial T^{-1}})_{p,c_{j},...}\] where I0 is the exchange current. At any overpotential η it is defined by the equation: \[U^{\ddagger }\left(\eta \right) = -R\ (\frac{\partial (\ln (|I|))}{\partial T^{-1}})_{p,\eta ,c_{j},...}\] where I is the current passing from the electrode into the electrolyte.
Source:
PAC, 1974, 37, 499. 'Electrochemical nomenclature' on page 516 (https://doi.org/10.1351/pac197437040499)