Abstract
We compute probability distributions of trajectory observables for reversible and irreversible growth processes. These results reveal a correspondence between reversible and irreversible processes, at particular points in parameter space, in terms of their typical and atypical trajectories. Thus key features of growth processes can be insensitive to the precise form of the rate constants used to generate them, recalling the insensitivity to microscopic details of certain equilibrium behavior. We obtained these results using a sampling method, inspired by the "s-ensemble" large-deviation formalism, that amounts to umbrella sampling in trajectory space. The method is a simple variant of existing approaches, and applies to ensembles of trajectories controlled by the total number of events. It can be used to determine large-deviation rate functions for trajectory observables in or out of equilibrium.
Highlights
Many growth and self-assembly processes result in patterns or structures that are not in thermal equilibrium. [1,2,3,4,5,6,7,8]
We found that at certain points in parameter space the properties of trajectory ensembles of these reversible and irreversible models were identical at the level of typical trajectories: both display a nonequilibrium critical point at which the trajectory ensemble exhibits a diverging susceptibility
We have shown that a simple method of rare-event sampling, motivated by the s-ensemble formalism and akin to an umbrella sampling of trajectories, can be used to sample the trajectory ensembles of models of reversible and irreversible growth
Summary
Many growth and self-assembly processes result in patterns or structures that are not in thermal equilibrium. [1,2,3,4,5,6,7,8]. We use the method to identify a connection between the trajectory ensembles of reversible and irreversible models of growth [19, 20] These models describe the evolution of a mean-field structure composed of two particle types. The method we use here is inspired by the dynamical large-deviation or s-ensemble formalism [24,25,26,27,28,29,30,31], but does not attempt to sample the s-ensemble Instead, it involves the use of a probability-conserving auxiliary or reference model [29] in which events that are rare in the original model are made typical, in order to allow efficient sampling of the relevant piece of the probability distribution.
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