The reordering kinetics of a diffusion lattice-gas system of adsorbates with nearest-and next-nearestneighbor interactions on a square lattice is studied within a dynamic Monte Carlo simulation, as it evolves towards the equilibrium from a given initial configuration, at a constant temperature. The diffusion kinetics proceeds through adsorbate hoppings to empty nearest-neighboring sites ͑Kawasaki dynamics͒. The Monte Carlo procedure allows a "real" time definition from the local transition

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... , and the configurational entropy and internal energy can be obtained from the lattice configuration at any instant t by counting the local clusters and using the C 2 approximation of the cluster variation method. These state functions are then used in their nonequilibrium form as a direct measure of reordering along the time. Different reordering processes are analyzed within this approach, presenting a rich variety of behaviors. It can also be shown that the time derivative of entropy ͑times temperature͒ is always equal to or lower than the time derivative of energy, and that the reordering path is always strongly dependent on the initial order, presenting in some cases an "invariance" of the entropy function to the magnitude of the interactions as far as the final order is unaltered.