Determination of Thermodynamic and Stochastic Potentials in Nonequilibrium Systems from Macroscopic Measurements

Abstract

For systems far from equilibrium, a potential determines the fluctuations from stable attractors, such as stationary states, and the thermodynamic approach to such states (Lyapunov function). For a reaction system with ionic reactions in a stationary state far from equilibrium, the imposition of a current displaces the system from that state. For such systems, we show that an electrochemical potential due to the imposed current, consisting of both a Nernstian term and a non-Nernstian term, directly yields the stochastic potential around its maximum to a good approximation, without knowledge of the reaction mechanism of the system. The approximation is good to the order of the percent difference between the Nernstian and non-Nernstian terms and can be used for evaluating the stochastic potential. For general systems, the imposition of a flow of intermediates also displaces the system from its stationary state to a new stationary state, which is a nonstationary state of the system without flow. The concentrations of the chemical species can be measured without time restraints, and by repeating various such displacements, sufficient data can be obtained to determine rate coefficients for a solution of a stationary master equation and its stochastic potential for a known or assumed reaction mechanism. Several experiments are suggested to test the consistency of the results with predictions of the master equation and, thus, to test that equation itself.