# Concentration Fluctuations from Multinomial Probability Theory and the possible role in continuum Microkinetic Rate Theory

## TL;DR

This paper uses multinomial probability theory to analytically describe concentration fluctuations in kinetic systems and investigates their potential role in deviations observed in continuum Microkinetic Rate Theory, finding fluctuations are not the cause.

## Contribution

It introduces an analytical framework based on multinomial probability theory for predicting concentration fluctuations and compares these predictions with kinetic Monte Carlo simulations.

## Key findings

- MPT accurately predicts canonical and grand canonical fluctuations.
- Fluctuations are shown not to be responsible for deviations in cMRT.
- Analytical expressions link fluctuations to average concentrations and sample sizes.

## Abstract

Recently, continuum Microkinetic Rate Theory (cMRT) has been advanced as a method of studying rates of systems, where deviations between observation and cMRT theory have been found, and it hypothesized that these deviations are linked either to oscillations or fluctuations. Multinomial probability theory (MPT) is used to derive analytical expressions for concentration fluctuations, giving the fluctuations as a function of average concentrations and sample sizes. MPT predictions of fluctuations in kinetically constrained systems are verified against kinetic Monte Carlo, and it analytically shown that MPT predicts canonical and grand canonical ensemble fluctuations. These fluctuation results are discussed in conjunction with cMRT deviations and it argued that fluctuations are not responsible for the deviations.

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Source: https://tomesphere.com/paper/1901.07376