title: First passage times in homogeneous nucleation: Dependence on the total number of particles.
abstract: Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory.
authors.affiliation: PRC INRA UMR85, CNRS UMR7247, Université François Rabelais de Tours, IFCE, F-37380 Nouzilly, France.
authors.forename: Romain
authors.initials: R
authors.lastname: Yvinec
authors.affiliation: Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan UMR5208, 69622 Villeurbanne, France.
authors.forename: Samuel
authors.initials: S
authors.lastname: Bernard
authors.affiliation: Departamento de Matemática, Universidad Federal de Campina Grande, Campina Grande, PB, Brazil.
authors.forename: Erwan
authors.initials: E
authors.lastname: Hingant
authors.affiliation: Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan UMR5208, 69622 Villeurbanne, France.
authors.forename: Laurent
authors.initials: L
authors.lastname: Pujo-Menjouet