How many is different? Ideal Bose gas revisited
How many H2O molecules are needed to form water?
While the precise answer is not known, it is clear that the answer should be a finite number.
It is hard to boil water if we fix the volume or density, whereas it becomes easy if we instead keep the pressure constant.
In the papers listed below, and summarized HERE, we have carefully revisited the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks.
We reported that the isobar of the ideal gas zigzags on the temperature-volume plane, as if boiling, provided the number of particles is finitely large enough such as 7616.
This may demonstrate for the first time how finite systems can feature mathematical singularities, realizing the notion of Emergence.
http://iopscience.iop.org/1367-2630/13/3/033003/ (Video abstract included)
http://pra.aps.org/abstract/PRA/v81/i6/e063636 (Canonical Ensemble, Numerical work)
http://pra.aps.org/abstract/PRA/v84/i2/e023636 (Analytic proof)