Theory of Determination of Thermodynamic and Stochastic Potentials from Macroscopic Measurements

For the first purpose we choose a chemical reaction system with some ionic species, as for example the minimal bromate reaction, for which we presented some experiments in Chap. 10. The system may be in equilibrium or in a nonequilibrium stationary state. An ion selective electrode is inserted into the chemical system and connected to a reference electrode. The imposition of a current flow through the electrode connection drives the chemical system (CS) away from its initial stationary state to a new stationary state of the combined chemical and electrochemical system (CCECS), analogous to driving the CS away from equilibrium in the same manner. A potential difference is generated by the imposed current, which consists of a Nernstian term dependent on concentrations only, and a non-Nernstian term dependent on the kinetics. We shall relate the potential difference to the stochastic potential; for this we need to know the ionic species present and their concentrations, but we do not need to know the reaction mechanism of the chemical system, nor rate coefficients.

For the second purpose we offer a suggestion for reaction systems with or without ionic species for an indirect method of determining the stochastic potential from macroscopic measurements. We impose an influx of any of the stable intermediate chemical species into the system (CS), and thus displace the CS from its initial stationary state to a new stationary state of the combined CS and the imposed influx. We measure the concentrations of species in the new stationary state and repeat this experiment for different imposed influx rates. We can fit these measurements to an assumed reaction mechanism and an assumed master equation to determine rate coefficients and the stochastic potential.