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This theoretical study demonstrates that Gibbs factorials, traditionally considered equilibrium statistical quantities, can appear as measurable kinetic observables in history-dependent chemical reactions. Using a model of AB₂ complex stabilization through single versus two-stage procedures, researchers show that the ratio of mean waiting times is governed by a combinatorial factor n_C!/[n_m!(n_C-n_m)!], where products formed at different stages are statistically distinguished despite being macroscopically identical. Molecular dynamics simulations confirm this predicted combinatorial scaling.
Why it matters
This finding bridges equilibrium statistical mechanics and non-equilibrium kinetics, potentially impacting how we understand and optimize multi-stage chemical synthesis and self-assembly processes. The ability to predict kinetic advantages from equilibrium probabilities could inform the design of more efficient reaction pathways in chemistry and materials science.
Understand the Science
arXiv:2503.13865v2 Announce Type: replace-cross
Abstract: Gibbs factorials are usually regarded as equilibrium counting factors. We show that they can also appear directly in a measurable kinetic observable when products formed at different stages are statistically distinguished in the history ensemble. In a model designed to isolate the essential ingredients, transient AB$_2$ complexes are stabilized as C molecules either in a single operation or through a two-stage procedure. The mean-waiting-time ratio is governed by a kinetic advantage factor $mathcal{A}_C$ defined from equilibrium probabilities. A fluctuation-theorem argument identifies the dominant contribution $n_{mathrm C}!/[n_{mathrm m}!(n_{mathrm C}-n_{mathrm m})!]$, where $n_{mathrm m}$ is the intermediate product number and $n_{mathrm C}$ is the final target. This Gibbs factorial arises because products formed before and after the intermediate operation are statistically distinguished in the history ensemble, although the final molecules are macroscopically identical. Molecular dynamics simulations confirm the predicted combinatorial scaling of the mean-waiting-time ratio.
Source: Gibbs Factorials Become Kinetic in History-Dependent Reactions