An alternative expression to the Sackur-Tetrode entropy formula for an ideal gas

• Published in: Chemical physics 2018-03, Vol.504, p.8-12
• Main Author: Nagata, Shoichi
• Format: Article
• Language: English
• Subjects: Fluctuation analysis; Ideal gas entropy; Sackur-Tetrode formula; Uncertainty relation
• ISSN: 0301-0104
• DOI: 10.1016/j.chemphys.2018.02.001

Entropy of a monoatomic ideal gas as a function of thermal uncertainty relation, which is denoted by (Δx)T(Δpx)T. [Display omitted] •A thermal uncertainty relation is defined and obtained.•This entropy of classical ideal gas is given in terms of thermal uncertainty relation.•An alternative expression to the Sackur-Tetrode entropy formula is given.•The entropy of classical ideal gas can be re-interpreted from a different perspective.•A bridge between entropy and the uncertainty relation in quantum state is provided. An expression for the entropy of a monoatomic classical ideal gas is known as the Sackur-Tetrode equation. This pioneering investigation about 100 years ago incorporates quantum considerations. The purpose of this paper is to provide an alternative expression for the entropy in terms of the Heisenberg uncertainty relation. The analysis is made on the basis of fluctuation theory, for a canonical system in thermal equilibrium at temperature T. This new formula indicates manifestly that the entropy of macroscopic world is recognized as a measure of uncertainty in microscopic quantum world. The entropy in the Sackur-Tetrode equation can be re-interpreted from a different perspective viewpoint. The emphasis is on the connection between the entropy and the uncertainty relation in quantum consideration.