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)