Riemannian metric in Gibbsian phase-space

Abstract

In the classical phase-space of Gibbs, a Riemannian line-element is defined, invariant under extended point transformations and preserving the Gbbsian volume. To make the line-element dimensionally homogeneous, Planck ’s constant h is incorporated in it. For a system consisting of particles, geodesics are investigated; they coincide with classical trajectories in the limit when h tends to zero, and have some interesting simple properties when h is finite.