Physics

Umbrella sampling

Trajectory

Rare events

Mathematics

Musical

Statistical physics

Statistics

Filter (signal processing)

Visual arts

Sampling (signal processing)

Rate function

Computer science

Molecular dynamics

Quantum mechanics

Formalism (music)

Applied mathematics

Computer vision

Observable

Large deviations theory

Physical review. E

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.

Rare behavior of growth processes via umbrella sampling of trajectories