  The generalized Langevin equation is widely used to model the influence of a
heat bath upon a reactive system. This equation will here be studied from a
geometric point of view. A dynamical phase space that represents all possible
states of the system will be constructed, the generalized Langevin equation
will be formally rewritten as a pair of coupled ordinary differential
equations, and the fundamental geometric structures in phase space will be
described. It will be shown that the phase space itself and its geometric
structure depend critically on the preparation of the system: A system that is
assumed to have been in existence for ever has a larger phase space with a
simpler structure than a system that is prepared at a finite time. These
differences persist even in the long-time limit, where one might expect the
details of preparation to become irrelevant.
