Mesoscience has recently been proposed as a possible general concept for describing complex systems far from equilibrium, however, concrete formulations are needed, and particularly, a statistical mechanics foundation of mesoscience remains to be explored. To this end, the mathematical theory of stochastic geometry is combined with the energy minimization multi-scale (EMMS) principle under the concept of mesoscience to propose a statistical mechanics framework. An EMMS-based particle velocity distribution function is then derived as an example to show how the proposed framework works, and more importantly, as a first key step toward a generalized kinetic theory for heterogeneous gas-solid flow. It was shown that the resultant EMMS-based distribution is bimodal, instead of the widely-used Maxwellian distribution, but it reduces to the Maxwellian distribution when the gas-solid system is homogeneous. The EMMS-based distribution is finally validated by comparing its prediction of the variance of solid concentration fluctuation and granular temperature with experimental data available in literature. (C) 2016 American Institute of Chemical Engineers