This paper generalizes the results of a recently developed kinetic theory of surface diffusion conceptually different both from the popular transition state hopping model and from the Fokker-Plank kinetic model (or its equivalent Generalized Langevin approach). Following the first principles of statistical mechanics, the theory is based on the evolution of the particle's probability density, and takes into account the possibility of a finite change in adparticle energy due to its interaction with the substrate excitations. We show how, in this general way under some simplifying assumptions, one can reach a relatively simple, analytical description of surface diffusion that goes far beyond the abilities of the TST model. Examples are given by the occurrence of long jumps and "anomalous" pre-exponential factors of the diffusion coefficient in the low-density limit. Moreover, the theory allows, for the first time, kinetic treatment of surface diffusion at inite occupancy, resulting in a new sight on mechanisms determining the density dependence of collective diffusivity. Some puzzling aspects of surface cluster diffusion (gliding) can also be elucidated.
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