@article{LIU2026, 
author = {Quanhui LIU},
title = {THE GEOMETRIC CONTACT AND ITS APPLICATIONS TO PHYSICS},
year = {2026},
journal = {Physics and Engineering},
volume = {36},
number = {3},
pages = {109-114},
keywords = {thermodynamics, statistical physics, differential geometry, contact, third law, Bose-Einstein condensation},
url = {https://www.sciopen.com/article/10.26599/PHYS.2026.9320313},
doi = {10.26599/PHYS.2026.9320313},
abstract = {Geometric contact provides a precise characterization of the approximate equality of two functions in physics, and its mathematical locality can be interpreted as physical intervality. In physics, the failure to introduce this geometric contact and provide it with a physical interpretation has led to unnecessary controversies in understandings and descriptions of the same phenomenon across various pieces of literature. By addressing two specific problems in thermodynamics and statistical physics, some long-standing unresolved conceptual issues have been resolved.}
}