Multi-excitation entropy: its role in thermodynamics and kinetics

TLDR

Multi‑excitation entropy (MEE) arises when large numbers of excitations fluctuate, such as during high‑barrier activation, and its significance in thermodynamics and kinetics is often overlooked despite its role in free‑energy and Arrhenius/Eyring descriptions. The review aims to examine experimental evidence for the Compensation Law, Isokinetic Rule, and Meyer–Neldel Rule, and to argue that MEE is crucial for understanding kinetics and thermodynamics when activation energies are large. The authors survey MNR observations across chemistry, physics, biology, and geology, and discuss how the MEE model fails for low‑activation‑energy or high‑temperature systems. The review presents evidence that the MEE model explains the Meyer–Neldel Rule, outperforming non‑entropic compensation models.

Abstract

This review concerns the concept of multi-excitation entropy (MEE) and its consequences. When a fluctuation involving a large number of excitations occurs, for example, when a large activation barrier is overcome, there must be a large entropy associated with this fluctuation. First, the concepts of free energy and entropy, of activated processes and the Arrhenius and Eyring equations are reviewed. The tendency to neglect entropy, whose value is difficult to determine, in modelling kinetic processes, is briefly discussed. We then present a review of the experimental observations of the phenomenon which is variously known as the Compensation Law, the Isokinetic Rule and the Meyer–Neldel Rule (MNR). These observations include examples from chemistry, condensed matter physics, biology and geology. Arguments are then presented for the importance of entropy and particularly of MEE in both kinetics and thermodynamics, when activation energies are large. After a discussion of non-entropic models of compensation, we present results which support the MEE model as an explanation of MNR. The behaviour of systems with low activation energies, or at high temperatures, to which the MEE model does not apply, is then discussed.