# Computational Efficiency and Amdahl's law for the Adaptive Resolution Simulation Technique

## TL;DR

This paper analyzes the computational efficiency of the adaptive resolution simulation technique in molecular dynamics, demonstrating that Amdahl's Law can accurately predict its performance within 10-15% accuracy.

## Contribution

It introduces a generalized predictive formula based on Amdahl's Law to estimate the efficiency of multiscale molecular simulations with reduced degrees of freedom.

## Key findings

- Efficiency estimate within 10-15% accuracy using Amdahl's Law
- The formula applies broadly to multiscale molecular dynamics approaches
- Adaptive resolution technique shows significant computational advantages

## Abstract

We discuss the computational performance of the adaptive resolution technique in molecular simulation when it is compared with equivalent full coarse-grained and full atomistic simulations. We show that an estimate of its efficiency, within $10-15\%$ accuracy, is given by the Amdahl's Law adapted to the specific quantities involved in the problem. The derivation of the predictive formula is general enough that it may be applied to the general case of molecular dynamics approaches where a reduction of degrees of freedom in a multiscale fashion occurs.