Microscopic and macroscopic systems

It is useful, at this stage, to make a distinction between the different sizes of the systems that we are going to examine. We shall call a system microscopic if it is roughly of atomic dimensions, or smaller. On the other hand, we shall call a system macroscopic when it is large enough to be visible in the ordinary sense. This is a rather inexact definition. The exact definition depends on the number of particles in the system, which we shall call $N$. A system is macroscopic if

$$\frac{1}{\sqrt{N}} \ll 1,$$

which means that statistical arguments can be applied to reasonable accuracy. For instance, if we wish to keep the statistical error below one percent then a macroscopic system would have to contain more than about ten thousand particles. Any system containing less than this number of particles would be regarded as essentially microscopic, and, hence, statistical arguments could not be applied to such a system without unacceptable error.