  Glass transition and random packing in the hard sphere system have attracted
great attention due to the important role of the system in the investigation of
diverse real systems including liquids, colloidal dispersions, supercooled
liquids, glasses and granular materials (1-12) Despite the importance and
simplicity of the system, some fundamental questions, such as the existence of
an ideal glass transition (5-16), the nature of the glass transition and random
packing (or jamming), and the entropy crisis or Kauzmann paradox (17,18),
remain open. Based on a very accurate equation of state over the entire stable
and metstable region within the potential energy landscape framework, here we
report two phase transitions observed in the hard sphere system: the first is
the ideal glass transition, indicating the configurational entropy vanishing,
and the second, the jamming transition between the random loose packing and the
random close packing 1,2 (or maximally random jammed packing (11,12)),
indicating inherent structure domination. However, it is suggested that the
glass and jamming transitions might not be treated as a thermodynamic phase
transition. The unbalanced entropy loss suggests that equilibrium
thermodynamics does not work for supercooled liquids and glasses. The results
presented here for the hard sphere system will have direct impact on studies
related to random packing or jamming and will shed a light on studies of glass
transition in real systems.
