## Quick Reference

A hypothesis in statistical mechanics concerning phase space. If a system of *N* atoms or molecules is enclosed in a fixed volume, the state of this system is given by a point in 6*N*-dimensional phase space with *q*_{i} representing coordinates and *p*_{i} representing momenta. Taking the energy *E* to be constant, a representative point in phase space describes an orbit on the surface *E*(*q*_{i},*p*_{i}) = *c*, where *c* is a constant. The ergodic hypothesis states that the orbit of the representative point in phase space eventually goes through all points on the surface. The **quasi-ergodic hypothesis** states that the orbit of the representative point in phase space eventually comes close to all points on the surface. In general, it is very difficult to prove the ergodic or quasi-ergodic hypotheses for a given system. See also ergodicity; KAM theorem.

*Subjects:*
Chemistry — Physics.