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.