TABLE OF CONTENTS Macroscopic properties can be computed from microscopic properties from equations like (2.7.3) only if the time ratios t n/( t 2 ? t 1) are known. But there is no way of computing these ratios, and time averages cannot be used to construct a practical statistical mechanics. An alternative to time averages is provided by the concept of ensembles.
Imagine an enormous number of systems all of which are replicas of the physical system under consideration and all subject to the same external conditions as the physical system. Now place imaginary walls around each system and stack them together to form one huge, continuous mass. Such a collection is called an ensemble, and each replica is a member system of the ensemble.
The nature of the boundaries between the systems determines the type of ensemble:
If the boundaries are impermeable and each system is completely isolated, there are no interactions among the systems and the ensemble is called microcanonical.
If the walls are permeable to energy but not to anything else, only energy can be transferred among systems and the ensemble is called canonical.
If both energy and matter can be exchanged among systems, but the walls are impermeable to all other influences, the ensemble is called grand canonical.
In the above three ensemble types, it is assumed that the volume of each member of the ensemble is the same. However, it is possible to define ensembles in which the volumes of...
