(Taken primarily from Ch. 2 of Frenkel and Smit [1] and Ch. 3 of Introduction to Modern Statistical Mechanics, by David Chandler [5].)
This course is centered upon one mathematical statement: \begin{equation} \label {eq:ensemble_average} \left \langle G\right \rangle = \sum _\nu P_\nu G_\nu \end{equation} That is, the expectation value, \(\left \langle G\right \rangle \), of some observable property \(G\) is an average over all possible microstates available to a system, indexed by \(\nu \), where \(P_\nu \) is the probability of observing the system in microstate \(\nu \), and \(G_\nu \) is the value of the measured property G when the system is in microstate \(\nu \). Eq. 1 illustrates the operation of performing an ensemble average.
Before even considering how to use computer simulation to make such a measurement of a particular property for a particular system, there are three main issues to consider:
In the following subsections, we give a cursory treatment of elementary statistical mechanics aimed at answering these questions. The aim is to give the student an appreciation (not a mastery) of the basic physics that underlies a majority of current molecular simulation.