Gibbs considered the following difficulty that arises if the ideal gas entropy is not extensive. Two containers of an ideal gas sit side-by-side. The gas in container #1 is identical in every respect to the gas in container #2 (i.e. in volume, mass, temperature, pressure, etc). Accordingly, they have the same entropy S. Now a door in the container wall is opened to allow the gas particles to mix between the containers. No macroscopic changes occur, as the system is in equilibrium. But if the formula for entropy is not extensive, the entropy of the combined system will not be 2 S. In fact, the particular non-extensive entropy quantity considered by Gibbs predicts additional entropy (more than 2 S). Closing the door then reduces the entropy again to S per box, in apparent violation of the Second Law of Thermodynamics.