Mapping the dynamics of reversible and irreversible heterogeneous electron transfers under steady-state conditions by the phase-space method

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

“…(47). Our previous work [16] indicated that the transfer coefficient a a can be determined from the following relationships: The above results show that irreversibility is not an intrinsic property of the system but a measure of some distance in terms of relative entropy and cross-entropy with respect to a reference, for instance, the reversible conditions. This distance reflects the value of the dimensionless spatio-temporal constant RKN that characterizes the dynamics of the system.…”

“…The evolution of the system under stationary conditions can be described as a diffusion process along the n coordinate characterizing the trajectory in the phase space. In the previous work [16], we have shown that…”

“…We consider an electrochemical reaction-diffusion system maintained at a fixed temperature. We study a simple heterogeneous electron transfer under the conditions of a stationary regime characterized by a probability density function Pðn; eÞ [16], where n and e are the degree of advancement and the dimensionless potential, respectively. It should be noted that the system under investigation (Scheme 1) is a driven system one which evolves via a series of non-equilibrium stationary states.…”

“…Under steady-state conditions, the fluxes of all species are constant and are equal to the specific value at the working electrode surface. In our previous work [16], we have introduced a dimensionless variable n ox that allows us to calculate the degree of advancement of the electro-oxidation described in Eq. (1) as:…”

“…It is a ratio of time constants, s diff and s het , that characterize mass transport (diffusion process) and heterogeneous electron transfer, respectively. These time constants are defined as follows [16]:…”