TABLE OF CONTENTS Consider a system containing a large number of atoms or molecules. If it were completely isolated, it would be in a definite quantum state. But no real system can be completely isolated, and no measurements can be made on an isolated system. If the interaction between the system and its environment is weak and random, then the environment is sufficiently constant, on the average, that it does not affect the measured properties of the system, at least within the accuracy of the macroscopic measurement. By a weak interaction, we mean that the changes in the system properties are very small compared to the value of those properties. By random, we mean that over the time it takes to make a measurement, there are a large number of changes in the properties of the system, that the magnitude of these changes follow the rules of probability for independent events, and that the effects of positive and negative changes are very nearly equal. Such an environment might consist of a heat bath at constant temperature that exchanges energy with the system. In addition, the system can be subject to small perturbations due to stray electric and magnetic fields, mechanical vibrations, cosmic rays, and so on. The microscopic state of the system is therefore changing in time in a random, chaotic manner, but its macroscopic state remains essentially unchanged. We will call such an environment one that is thermodynamically constant.
If the environment is not weak or not...
