Theory of Bose‐Einstein Fluids, Statistical Mechanical Treatment of the Thermodynamic Properties of Liquid Helium

A formal development of the difference in thermodynamic properties of a Bose‐Einstein and a hypothetical Boltzmann system is presented. The treatment is valid for any thermodynamic phase of the two systems, including the liquid phase to which it is intended to apply. The formal equations show the change in activity of the liquid‐gas and crystal‐liquid transitions for the two systems. A transition, which we identify with the lambda transition in liquid helium is predicted. By reasonable choice of a reduced mass parameter the lambda line can be correctly located. The nature of the lambda transition is related to the behavior at its singularity, of a series, the nth coefficient of which is a defined integral of functions of coordinates of n molecules. The simplest assumption which can be made to permit integration does not lead to the correct order of the transition.