Grain coarsening is a phenomenon common to all polycrystalline materials at elevated temperatures. During the last 50 years a number of sophisticated models have been developed for grain-coarsening kinetics. The authors have shown that Onsager's extremal principle represents a systematic way of deriving evolution equations for parameters characterizing thermodynamic systems. If the grain radii are chosen as those parameters, the application of Onsager's principle reproduces Hillert's classical evolution equations for the radii of individual grains (multigrain concept). The observed or calculated ensemble of grains is usually classified by a grain radii distribution function involving a certain number of parameters. The novelty of the paper is represented by the direct application of Onsager's principle to the radii distribution function by derivation of the evolution equations for its parameters (distribution concept). The kinetics of systems with bimodal and different monomodal starting distribution functions are calculated by means of both multigrain and distribution concepts, and the results of simulations are compared and discussed. The dissipation of the grain coarsening process is evaluated, and it is shown that the width of the distribution function decisively influences the coarsening kinetics.