Revisiting Kinetic Monte Carlo Algorithms for Time-dependent Processes: from open-loop control to feedback control

TL;DR

This paper introduces a unified analysis of kinetic Monte Carlo algorithms for time-dependent stochastic systems, extending them to include feedback control, and presents a new algorithm that accurately models feedback-controlled dynamics without artifacts.

Contribution

It provides a unified proof and tutorial for existing open-loop KMC algorithms and introduces a novel feedback-controlled KMC method that accurately captures system dynamics.

Findings

Unified analysis and proof of existing KMC algorithms.

New feedback-controlled KMC algorithm that avoids Zeno effect.

Accurate simulation of feedback-controlled stochastic systems.

Abstract

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to time-dependent stochastic systems. Based on this analysis, we revisit several time-dependent kinetic Monte Carlo (KMC) algorithms designed for systems under open-loop-control protocols. Our analysis provides an unified alternative proof to these algorithms, summarized into a pedagogical tutorial. Moreover, with the trajectory probability analysis, we present a novel feedback-controlled KMC algorithm that accurately captures the dynamics systems controlled by external signal based on measurements of the system's state. Our method correctly captures the system dynamics and avoids the artificial Zeno effect that arises from incorrectly applying the direct Gillespie algorithm to feedback-controlled systems. This work provides a unified perspective on existing open-loop-control KMC algorithms and also offers a powerful and accurate tool for simulating stochastic systems with feedback control.