Neumann notation

In mathematical thermodynamics, Neumann notation refers to the use of the d hat symbol used to signify that the differential is an inexact differential, predominately used for differentials of heat and work, as compared to an exact differential.

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 \bar{d} \,1875Carl Neumann(add: comment)
Lectures on the Mechanical Theory of Heat
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δ1924James PartingtonThe symbol δ to denotes that “δQ and δA are not perfect differentials, since each depends on the path of change.”Chemical Thermodynamics

To note, Partington footnotes this statement, directing readers to his 1920 Higher Mathematics for Chemical Students, in which he says that he gives a proper treatment of the properties of perfect differentials, as presented by Rudolf Clausius (1875). [2]

Etymology
The term "Neumann notation", an Hmolpedia coining, is indicative of the fact that the d hat notation was specifically introduced by German mathematician Carl Neumann in his 1875 Lectures on the Mechanical Theory of Heat to signify inexact differentials.

References
1. (a) Neumann, Carl. (1875). Vorlesungen über die mechanische Theorie der Wärme (Lectures on the Mechanical Theory of Heat). Germany.
(c) Anon. (1877). “Science (Review: Lectures on the Mechanical Theory of Heat by Carl Neumann, 1875)”, The Westminster Review (pg. 250-), Jan-Apr.
(b) Laider, Keith, J. (1993). The World of Physical Chemistry. Oxford University Press.
2. Partington, James. (1920). Higher Mathematics for Chemical Students (§§ 55, 115). London.

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