Glass transition and random packing in the hard sphere system
  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. 
Hongqin Liu