On the energy distribution function for a one-dimensional gravitational system

The fractional energy distribution N(E), the possible importance of which has recently been studied by Binney, is studied here for the case of a one-dimensional gravitational system. In equilibrium, N(E) is effectively found to obey a Boltzmann law; in the dynamical evolution, far from being a conserved quantity, N(E) relaxes as violently as and fluctuates more strongly than the virial ratio. (author)