How many is different? Answer from ideal Bose gas
arXiv:1310.5580 · doi:10.1088/1742-6596/490/1/012018
Abstract
How many molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit.
4 pages and 2 figures. Prepared for a conference proceeding, IC-MSQUARE, Prague, Czech Republic, September 1-5, 2013