Each set of three panels represents the behaviour, the entropy history, and the enrgy distribution of two two-dimensional perfectly elastic balls in an enclosed box that also contains other balls. In the left panel, the yellow and the red ball constitute the universe whose energy and entropy relations are examined. The blue balls represent the world outside, with which the yellow and red can interact. The universe of red and yellow balls is not isolated (except in the case where there are no blue balls).
The middle panel in each group of three has three graphs, to which a new point is added every time there is a collision involving a red or yellow ball. The black line represents the total energy of the universe of the red and yellow balls, the red line the entropy of that universe, and the blue line the entropy relative to the maximum entropy available at the energy of the moment. If there are no blue balls, the energy remains constant, and the actual and relative entropies are the same (they are plotted with an arbitrary vertical displacement on the plots.
The right-hand panel with the green arcs shows a new point after each time a collision involves the universe of interest. The X-axis represents the velocity of the yellow ball, the Y-axis that of the red ball after the collision. When the universe is closed, its energy does not change, and the dots all fall on a single circular arc centred on the origin. If there is one blue ball, and a third axis had been plotted pointing out of the screen, all the points would fall on the surface of a sphere centred at the origin, but what is plotted is the projection of the 3-sphere onto the plane. When there are more blue balls, the projection onto the plane is of points on a hypersphere of dimension equal to the total number of balls. Always, the square of the distance of the red dot from the origin is the total energy in the universe of the red and yellow balls.
The important thing to notice is that entropy does not always increase, even in a closed universe.
Key for the middle panel graphs:
Scales have been shifted an arbitrary amount vertically.