How many is different? Answer from ideal Bose gas
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.
Cite
@article{arxiv.1310.5580,
title = {How many is different? Answer from ideal Bose gas},
author = {Jeong-Hyuck Park},
journal= {arXiv preprint arXiv:1310.5580},
year = {2014}
}
Comments
4 pages and 2 figures. Prepared for a conference proceeding, IC-MSQUARE, Prague, Czech Republic, September 1-5, 2013