# Convergence of metadynamics: discussion of the adiabatic hypothesis

## TL;DR

This paper investigates the long-term convergence of the metadynamics algorithm under the adiabatic assumption, analyzing the effects of decoupled dynamics and biases when this assumption is violated.

## Contribution

It provides a theoretical discussion on the convergence of metadynamics and explores the impact of the adiabatic hypothesis and its violations.

## Key findings

- Convergence of metadynamics under adiabatic conditions.
- Analysis of bias introduced when adiabatic assumption fails.
- Parallel between metadynamics and polymer self-interacting models.

## Abstract

By drawing a parallel between metadynamics and self interacting models for polymers, we study the longtime convergence of the original metadynamics algorithm in the adiabatic setting, namely when the dynamics along the collective variables decouples from the dynamics along the other degrees of freedom. We also discuss the bias which is introduced when the adiabatic assumption does not holds.