This course is centered upon a mathematical statement called an “ensemble average”: \begin{equation} \label {eq:ensemble_average} \left <G\right > = \sum _\nu P_\nu G_\nu \end{equation} That is, the expectation value, \(\left <G\right >\), 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 \(\nu \). 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 elmentary statistical mechanics aimed at answering these questions. The aim is to give the student an appreciation of the basic physics that underlies a majority of current molecular simulation.