A hypothesis in statistical mechanics concerning phase space, which was stated by Ludwig Boltzmann in 1887. 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 6N-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, which was stated by Enrico Fermi in 1923, asserts 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.