6 - Computer simulation algorithms

Summary

Introduction

Linear response theory can be used to design computer simulation algorithms for the calculation of transport coefficients. There are two types of transport coefficients: mechanical and thermal, and we will show how thermal transport coefficients can be calculated using mechanical methods.

In Nature nonequilibrium systems may respond essentially adiabatically, or depending upon circumstances, they may respond approximately isothermally — the quasi-isothermal response. No natural systems can be precisely adiabatic or isothermal. There will always be some transfer of the dissipative heat produced in nonequilibrium systems towards thermal boundaries. This heat may be radiated, convected, or conducted to the boundary reservoir. Provided this heat transfer is slow on a microscopic timescale and provided that the temperature gradients implicit in the transfer process lead to negligible temperature differences on a microscopic length scale, we call the system quasi-isothermal. We assume that quasi-isothermal systems can be modelled microscopically in computer simulations, as isothermal systems.

In view of the robustness of the susceptibilities and equilibrium time-correlation functions to various thermostatting procedures (see Sections 5.2 and 5.4), we expect that quasi-isothermal systems may be modeled using Gaussian or Nosé—Hoover thermostats or enostats. Furthermore, since heating effects are quadratic functions of the thermodynamic forces, the linear response of nonequilibrium systems can always be calculated by analyzing the adiabatic, isothermal, or isoenergetic response.