Statistical Mechanics for Engineers

Abstract

The purpose of writing this book is to explain basic concepts of equilibrium statistical mechanics to the first year graduate students in engineering departments. Why should an engineer care about statistical mechanics? Historically, statistical mechanics evolved out of the desire to explain thermodynamics from fundamental laws of physics governing behavior of atoms and molecules. If a microscopic interpretation of the laws of thermodynamics were the only outcome of this branch of science, statistical mechanics would not appeal to those of us who simply wish to use thermodynamics to perform practical calculations. After all, validity of thermodynamics has long been established. In thermodynamics, a concept of fundamental equations plays a prominent role. From one such equation many profound predictions follow in a completely general fashion. However, thermodynamics itself does not predict the explicit form of this function. Instead, the fundamental equation must be determined empirically for each system of our interest. Being a science built on a set of macroscopic observations, thermodynamics does not offer any systematic way of incorporating molecular level information, either. Thus, an approach based solely on thermodynamics is not sufficient if we hope to achieve desired materials properties through manipulation of nanoscale features and/or molecular level architecture of materials. It is in this context that the method of statistical mechanics becomes important for us. Equilibrium statistical mechanics provides a general framework for constructing the fundamental equation from a molecular level description of the system of interest. It can also provide a wealth of molecular level insights that is otherwise inaccessible even experimentally. As such, it is becoming increasingly more relevant to engineering problems, requiring majority of engineering students to develop more than just a passing acquaintance with the basic results of this subject.