Macrostates and Microstates

In describing a system made up of a great many particles, it is usually possible to specify some macroscopically measurable independent parameters, $x_1$ , $x_2, \cdots, x_n$ , that affect the particles' equations of motion. These parameters are termed the external parameters of the system. Examples of such parameters are the volume (this gets into the equations of motion because the potential energy becomes infinite when a particle strays outside the available volume), and any applied electric and magnetic fields. A microstate of the system is defined as a state for which the motions of the individual particles are completely specified (subject, of course, to the unavoidable limitations imposed by the uncertainty principle of quantum mechanics). In general, the overall energy of a given microstate, $r$ , is a function of the external parameters:

$$E_r \equiv E_r(x_1, x_2, \cdots, x_n).$$ (4.6)

A macrostate of the system is defined by specifying the external parameters, and any other constraints to which the system is subject. For example, if we are dealing with an isolated system (i.e., one that can neither exchange heat with, nor do work on, its surroundings) then the macrostate might be specified by giving the values of the volume and the constant total energy. For a many-particle system, there are generally a very great number of microstates that are consistent with a given macrostate.