Statistical interpretation of 10−24 moles and less

Abstract

A few examples of systems in thermodynamic equilibrium are cited in the classic text of Lewis and Randall [Thermodynamics (McGraw-Hill, New York, 1960)] which are problematic in that classical thermodynamics predicts the presence of a very small fraction of a single atom in a given form, e.g., tungsten vapor present in equilibrium with solid at 100 °C (p≂10−105 atmosphere). Lewis and Randall state, however, that the vapor pressure of a normal system, e.g., water at room temperature and that of tungsten at 100 °C, can be used ‘‘with the same sense of security.’’ They do not elaborate further. The problem is analyzed from first principles and it is pointed out that the apparent incongruity in having a fractional atom is removed in the density matrix description of the equilibrium state. A description of the equilibrium state that avoids the concept of a ‘‘fractional atom’’ has to identify the equilibrium property as a time average. The shortcoming of such a description is pointed out.