Information theory for analyzing heterogeneous electron transfer dynamics under steady-state conditions

We develop a methodology based on information theory for studying the general characteristics of an electrochemical system from partial and incomplete information. We characterize a simple heterogeneous electron transfer under the conditions of a stationary regime in terms of a probability density function. This probability density function, which represents the observer’s state of knowledge about the system rather than the state of the system itself, allows calculation of the information or statistical entropy. We show that irreversibility is not an intrinsic property of the system but a measure of some distance depending upon the relative entropy or Kullback–Leibler entropy and cross-entropy with respect to a reference, for instance, reversible conditions. The value of this distance is mainly determined by the ratio of two time constants characterizing the dynamics of the system. Data on ferrocene and ferric ions obtained in ultramicroelectrode experiments are given to illustrate the proposed methodology. Our objectives here are to present a different perspective on heterogeneous electron transfer reactions based on the information theory, and how the resulting formalism may be used to interpret experimental data.