Physical Limits on the Notion of Very Low Temperatures

Standard statistical thermodynamic views of temperature fluctuations predict a magnitude $(\sqrt{<(\Delta T)^2>}/T)\approx\sqrt{(k_B/C)}$ for a system with heat capacity $C$. The extent to which low temperatures can be well defined is discussed for those systems which obey the thermodynamic third law in the form $\lim_{(T\to 0)}C=0$. Physical limits on the notion of very low temperatures are exhibited for simple systems. Application of these concepts to bound Bose condensed systems are explored, and the notion of bound Boson superfluidity is discussed in terms of the thermodynamic moment of inertia.