Attempted to clarify thermodynamic limit a little more.

Author: JIMonroe

paper/basic_training.tex

@@ -228,7 +228,7 @@ \subsubsection{Key concepts}
 The concept of the thermodynamic limit is particularly important here.
 Specifically, as the size of a finite system is increased, keeping the particle number density roughly constant, at some point it is said to reach the thermodynamic limit where its behavior is bulk-like and no longer depends on the extent of the system.
 Thus, small systems will exhibit unique behaviors that reflect their microscopic size, but sufficiently large systems are said to have reached the thermodynamic limit and macroscopic thermodynamics applied.
-This is due to the fact that the effect of interfaces or boundaries have largely been removed, and that averages of system properties are now over a sufficiently large number of molecules that any instantaneous snapshot of the system roughly corresponds to average behavior (i.e. fluctuations in system properties become negligible).
+This is due to the fact that the effect of interfaces or boundaries have largely been removed, and, more importantly, that averages of system properties are now over a sufficiently large number of molecules that any instantaneous snapshot of the system roughly corresponds to average behavior (i.e. fluctuations in properties become negligible with increasing system size).
 
 Although we usually think of thermodynamics applying macroscopically and statistical mechanics applying on the microsopic level, it is important to remember that the laws of thermodynamics still hold \textit{on average} regardless of the length scale.
 That is, a molecule in contact with a thermal bath will exchange energy with the bath, but its average energy is a well-defined constant.