Physical Limits on the Notion of Very Low Temperatures

TL;DR

This paper investigates the fundamental physical limits of defining very low temperatures in thermodynamic systems, especially as they approach absolute zero, and explores implications for Bose condensed systems and superfluidity.

Contribution

It introduces a framework for understanding the limits of temperature definition near absolute zero, considering the third law of thermodynamics and applying it to Bose condensed systems.

Findings

Temperature fluctuations diminish as T approaches zero.

Physical bounds on temperature definition are derived for simple systems.

Implications for Bose superfluidity are discussed.

Abstract

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.