Birkhoff Theorem and Ergometer: Relationship by an Existence Assumption

By means of the recently developed ergometer, Birkhoff's theorem is made physically useful. In particular, the conditions of the theorem are given an interpretation through a many-body model which exhibits both ergodic and nonergodic behavior depending on the range of a certain parameter of the model. To our knowledge these illustrations are the first known examples of the use of Birkhoff's theorem in many-body theory. (author)