Extensivity and the thermodynamic limit: Why size really does matter

The thermodynamic limit and extensivity are central concepts in thermodynamics. In this paper, these are critically examined in light of systems for which they appear inadequate. It is found that their limitations lead to counterintuitive thermodynamic results involving heat flow, phase separations, thermostatistics of gravitating systems and the conversion efficiency of heat into work. Ultimately, these limitations are shown to bear on the utility of entropy and the universality of the second law of thermodynamics.