# Reaction kinetics in the few-encounter limit Source: [Reaction kinetics in the few-encounter limit]() Collection index: [llms.txt]() Data updated: 2025-10-25T00:21:47.940Z Authors: David Hartich, Aljaz Godec Published: 2019-01-28T17:08:48.000Z ## Abstract The classical theory of chemical reactions can be understood in terms of diffusive barrier crossing, where the rate of a reaction is determined by the inverse of the mean first passage time (FPT) to cross a free energy barrier. Whenever a few reaction events suffice to trigger a response or the energy barriers are not high, the mean first passage time alone does not suffice to characterize the kinetics, i.e., the kinetics do not occur on a single time-scale. Instead, the full statistics of the FPT are required. We present a spectral representation of the FPT statistics that allows us to understand and accurately determine FPT distributions over several orders of magnitudes in time. A canonical narrowing of the first passage density is shown to emerge whenever several molecules are searching for the same target, which was termed the 'few-encounter limit'. The few-encounter limit is essential in all situations, in which already the first encounter triggers a response, such as misfolding-triggered aggregation of proteins or protein transcription regulation. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()