Introduction The Merger of Classical Mechanics and Probability Theory

1 Introduction The Merger of Classical Mechanics and Probability Theory 

it should be clear that we have introduced the word average in our discussion, and certainly we have used it rather loosely. Averages 

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The merger of probability theory and classical mechanics is accomplished by the so-called Liouville equation, which is considered to he the fiindamental equation of statistical mechanics. From this equation we can obtain a comprehensive description of both the equilibrium and nonequilibrium behavior of matter. In this chapter, we will derive the famous Liouville equation from a simple differential mass balance approach. In this case, the mass will represent a S3rstem of points in a multidimensional space. Each point contains all the information about the system at a particular time. The Liouville equation obtained here will be called upon in each of the subsequent chapters in our quest to describe the observed behavior and properties of any particular system. 

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