On the time and cell dependence of the coarse-grained entropy. II

We present calculations of the coarse-grained entropy Scg(t) for the model of a classical point particle enclosed in a two-dimensional box with perfectly reflecting walls. We find in comparison with the one-dimensional case that the fluctuations of Scg(t) and of the expectation values of the position have decreased, and that Scg(t) does not take its asymptotic value at regular time intervals. The times after which Scg(t) and the expectation values have approximately reached their equilibrium values, are about equal; recurrence times are rather clearly separated from this time. Finally, we give a general estimate on the change of an expectation value due to a refinement of the cells.