  I show how the Fermi and Bose pressures in quantum systems, identified in
standard discussions through the use of thermodynamic analogies, can be derived
directly in terms of the flow of momentum across a surface by using the quantum
mechanical stress tensor. In this approach, analogous to classical kinetic
theory, pressure is naturally defined locally, a point which is obvious in
terms of the stress-tensor but is hidden in the usual thermodynamic approach.
The two approaches are connected by an interesting application of boundary
perturbation theory for quantum systems. The treatment leads to a simple
interpretation of the pressure in Fermi and Bose systems in terms of the
momentum flow encoded in the wave functions. I apply the methods to several
problems, investigating the properties of quasi continuous systems, relations
for Fermi and Bose pressures, shape-dependent effects and anisotropies, and the
treatment of particles in external fields, and note several interesting
problems for graduate courses in statistical mechanics that arise naturally in
the context of these examples.
