How many is different? Answer from ideal Bose gas

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Park, Jeong-Hyuck^1,2

Department of Applied Mathematics and Theoretical Physics, CB3 0WA Cambridge, United Kingdom^1

Department of Physics, Sogang University, Seoul 121-742, Korea, Republic of^2

关键词: Finite number;    Finite systems;    H2O molecules;    Ideal Bose gas;    Ideal gas;    Thermodynamic limits;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012018/pdf
DOI  :  10.1088/1742-6596/490/1/012018

来源: IOP

【 摘 要 】

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 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.