see Roederer (2005), section 5.5). Consider two vessels [A]{} and [B]{} of equal volume, joined by a tube with a closed valve, thermally isolated and filled with the same gas at the same pressure and temperature. If we open the valve, nothing will happen thermodynamically, but at the microscopic level, we can picture in our mind the molecules of [A]{} expanding into vessel [B]{} and the molecules of [B]{} expanding into [A]{}. Each process would represent an adiabatic expansion with an increase of the entropy by $-k N \ln{2}$ (where $k$ is Boltzmann’s constant and $N$ is the number of molecules in [A]{} or [B]{}), so there should be a total increase of the entropy of the system by ${\Delta S=-2 k N \ln{2}}$. This of course is absurd and represents Gibbs’ paradox. In most textbooks it is (somewhat lamely) explained away by saying that the formulas used here are indeed correct, but apply *only* if the gases in the two vessels are *physically distinguishable*[^6] (different gases, or just specimens of opposite chirality).

So what is wrong with the conclusions of the above thought experiment? By invoking the concept of pragmatic information when we say that “we can picture in 