What good is the thermodynamic limit?

Scientific article / American Journal of Physics, 2004, Vol. 72, pp. 25–29.Statistical mechanics applies to large systems: technically, its results are exact only for infinitely large systems in 'the thermodynamic limit'. The importance of this proviso is often minimized in undergraduate courses. This paper presents six paradoxes in statistical mechanics that can be resolved only by acknowledging the thermodynamic limit. For example, it demonstrates that the widely used microcanonical 'thin phase space limit' must be taken after taking the thermodynamic limit.