Chapter Six Specification of the State of a System

1. We must establish a detailed method of describing the states of a system. This means that we must have a detailed way of describing the precise microstates in which a system can be found (or, equivalently, the precise outcome of a single experiment such as the toss of a die), as well as a precise way to describe the various macrostates of a system. 2. We must describe the system in terms of an ensemble of similar systems (that is, a large number of similarly performed tosses of the die, one right after another, or an infinitely large number of equivalent tosses taking place at one instant). This would seem to imply that we do not concern ourselves with an description of the system (such as the exact way in exact which a coin is tossed or a single die is thrown from which we could, in principle, predict the outcome). Rather, we concern ourselves only with a statistical description of what we might expect when each experiment is carried out under similar circumstances. 3. We assume that all of the possible microstates are equally likely. There is no real basis for this assumption. It is an assumption, i.e., one which is assumed in advance and a priori which is later shown to be true or false by examining predictions based upon this assumption. Thus far, this assumption seems to work very well! 4. We must use the mathematics of probability and statistics to determine the relative likelihood of the outcome of the experiments under study. Those systems which have a large number of microstates corresponding to a given macrostate will be most probable those with a small number of microstates corresponding to a given macrostate will be least probable.