From Hard Spheres and Cubes to Nonequilibrium Maps with Thirty-Some Years of Thermostatted Molecular Dynamics

TL;DR

This paper reviews the evolution of molecular dynamics simulations from simple models to complex systems, emphasizing the importance of simplicity and relevance in understanding statistical mechanics through computational methods.

Contribution

It highlights the progression of simulation techniques over thirty years, focusing on simple models to gain fundamental insights into statistical mechanics and thermodynamics.

Findings

Reproducibility in simple models aids understanding

Advances in algorithms have replaced formal theoretical approaches

Simple models like hard spheres and maps reveal fundamental principles

Abstract

This is our current research perspective on models providing insight into statistical mechanics. It is necessarily personal, emphasizing our own interest in simulation as it developed from the National Laboratories' work to the worldwide explosion of computation of today. We contrast the past and present in atomistic simulations, emphasizing those simple models which best achieve reproducibility and promote understanding. Few-body models with pair forces have led to today's "realistic" simulations with billions of atoms and molecules. Rapid advances in computer technology have led to change. Theoretical formalisms have largely been replaced by simulations incorporating ingenious algorithm development. We choose to study particularly simple, yet relevant, models directed toward understanding general principles. Simplicity remains a worthy goal, as does relevance. We discuss hard-particle virial series, melting, thermostatted oscillators with and without heat conduction, chaotic dynamics, fractals, the connection of Lyapunov spectra to thermodynamics, and finally simple linear maps. Along the way we mention directions in which additional modelling could provide more clarity and yet more interesting developments in the future.