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

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.