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We investigate the statistical mechanics of glass-forming materials andjamming matter by means of a geometrically driven approach based on a revisedcell theory. By considering the system as constituted of jammed blocks ofincreasing sizes, we obtain a unified picture that describes accurately thewhole process from low densities to limit densities at the glass/jammingtransition. The approach retrieves many of the aspects of existing theoriesunifying them into a coherent framework. In particular, at low densities wefind a free volume regime, based on local relaxation process, at intermediatedensities a cooperative length sets in, where both local and cooperativerelaxation process are present. At even higher densities the increasingcooperative length suppresses the local relaxation and only the cooperativerelaxation survives characterized by the divergence of the cooperative length,as suggested by the random first order theory. Finally a relation between thecooperative length and the hyperuniform length is also suggested.

Cell theory for glass-forming materials and jamming matter, combining free volume and cooperative rearranging regions