  We provide a comprehensive picture of the jamming phase diagram by connecting
the athermal, granular ensemble of jammed states and the equilibrium fluid
through the inherent structure paradigm for a system hard discs confined to a
narrow channel. The J-line is shown to be divided into packings that are
thermodynamically accessible from the equilibrium fluid and inaccessible
packings. The J-point is found to occur at the transition between these two
sets of packings and is located at the maximum the inherent structure
distribution. A general thermodynamic argument suggests that the density of the
states at the configurational entropy maximum represents a lower bound on the
J-point density in hard sphere systems. Finally, we find that the granular and
fluid systems only occupy the same set of inherent structures, under the same
thermodynamic conditions, at two points, corresponding to zero and infinite
pressures, where they sample the J-point states and the most dense packing
respectively.
