In thermodynamics, Carl Neumann (1832-1925) was a German mathematical physicist noted for his 1875 Lectures on the Mechanical Theory of Heat in which he introduction of the now-standard symbol notation $\bar{d} \,$ (d-hat), otherwise known as Neumann notation, or δ (Greek delta), in latter usages by others, to represent an inexact differential, i.e. one that is path dependent, such as are differentials of heat δQ and work δW. [1]

Neumann supposedly used his own methods, by passing the need for introducing the entropy function, to script his own version of thermodynamics. [2] His book on heat supposedly used methods on heat similar to German physicist Gustav Kirchhoff. [5]

Neumann seems to have developed an interested in thermodynamics via the overlap of heat and electricity. His 1873 book Explanation of Electrical Forces and Expansion gives evidence to this. [2] Neumann thought that mechanical explanations in physics were incomplete, contradictory, and overly complex. Having studied the analogies between electrodynamics and mechanics, specifically hydrodynamics, which Hermann Helmholtz, Gustav Kirchhoff, and Ludwig Boltzmann, and others had developed, Neumann convinced himself that the analogies lacked “deep foundations”. Moreover, the explanation of heat phenomena requires thermal principles and since heat is intimately related to electricity, he did not expect “merely mechanical principles” to succeed with electricity either. [2]

Inexact differential

See main: Inexact differential

German physicist Georg Helm seems to have been the first to point this origin out, specifically in his 1898 History of Energetics, wherein he comments Neumann was the one that suggested that the special differential sign $\bar{d}Q \,$ (d hat Q) should be used as a way of always keeping in mind the differentials, such as heat, that do not fit the condition for an exact differential. [8]

Economic thermodynamics
Neumann, supposedly, had views on how thermodynamics applied to economy. [6] Neumann argued that all economic life could be expressed by an exchange of energy or by “the transfer of energy of physical bodies”. Neumann, according to the 1887 views of Georg Helm, considered the “energy of the self as the capital of the body”, such that the body contained an energetic component considered as a commodity. [7] The actual citation used by Helm, in the Final Section to his The Doctrine of Energy is:

"Carl Neumann nennt die eigenenergie gelegentlich das Kapital des Körpers, und dass bei der Ausbildung der Energievorstellungen wirtschaftliche Analogien mitgewirkt haben, ist S. 18 von mir hervorgehoben worden (78)." Note 78 Bezeichnend sind die Worte, die Du Bois Reymond (Berl. Monatsberichte 1870) von Leibniz anführt: „Les forces ne sont (pas) detruites, mais dissip6es parmi les parties menues. Ce n'est pas les perdre, mais c'est faire comme font ceux, qui changent la grosse monnaie en petite." Sie sind eben so merkwürdig hinsichtlich des Dissipationsgedankens, wie hinsichtlich der wirtschaftlichen Analogie.	"Carl Neumann sets out on occasional discussion of the internal energy capital of the body, and that have participated in the training of energy performances economic analogies, p. 18 worden is highlighted by me (78)." Note 78 Typical are the words quoted by Du Bois Reymond (Berl. monthly reports in 1870) by Leibniz: "The forces are (not) destroyed, but among the minor parties disperses. This is not to lose them, but do like are those that change the currency in small wide." They are just as curious as to the Dissipationsgedankens as economic terms the analogy.

"Carl Neumann nennt die eigenenergie gelegentlich das Kapital des Körpers, und dass bei der Ausbildung der Energievorstellungen wirtschaftliche Analogien mitgewirkt haben, ist S. 18 von mir hervorgehoben worden (78)."

Note 78

Bezeichnend sind die Worte, die Du Bois Reymond (Berl. Monatsberichte 1870) von Leibniz anführt: „Les forces ne sont (pas) detruites, mais dissip6es parmi les parties menues. Ce n'est pas les perdre, mais c'est faire comme font ceux, qui changent la grosse monnaie en petite." Sie sind eben so merkwürdig hinsichtlich des Dissipationsgedankens, wie hinsichtlich der wirtschaftlichen Analogie.

"Carl Neumann sets out on occasional discussion of the internal energy capital of the body, and that have participated in the training of energy performances economic analogies, p. 18 worden is highlighted by me (78)."

Note 78

Typical are the words quoted by Du Bois Reymond (Berl. monthly reports in 1870) by Leibniz: "The forces are (not) destroyed, but among the minor parties disperses. This is not to lose them, but do like are those that change the currency in small wide." They are just as curious as to the Dissipationsgedankens as economic terms the analogy.

The term 'eigenenergy' (of translated as self-energy) may actually mean internal energy, possibly, as used in the sense of Helm? The exact article (or book) that Helm made these economic speculations using thermodynamic theory still needs to be tracked down; but, nevertheless, the above quote does seem to indicate that Neumann's thermo-economic views predate those of Helm?

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. Aris, Rutherford, David, Howard T, and Stuewer, Roger H. (1983). Springs of Scientific Creativity: Essays on the Founders of Modern Science (ch. 5: The Scientific Style of Josiah Willard Gibbs, pgs. 142-62; esp. pg. 150). University of Minnesota Press.
3. Ampere, A., Neumann F., Weber W., and Kirchhoff, G. (1873). Elektrischen Krafte Darlegung und Erweiterung der von A. Ampere, F. Neumann, W. Weber, G. Kirchhoff, Entwickelten Mathematischen Theorieen (Explanation of Electrical Forces and Expansion on the Mathematical Theories of A. Ampere, F. Neumann, W. Weber, and G. Kirchhoff). Leipzig.
4. (a) Jungnickel, Christa. (1986). Intellectual Mastery of Nature: Theoretical Physics form Ohm to Einstein, Volume 2, 1870-1925 (Footnote 53: pg. 228). University of Chicago Press.
(b) Neumann, Carl. (1873?) Beitrage zu einzelnen Theilen der Mathematischen Physik, insbesondere zur Elektordynamik und Hydrodynamik, Elektrostatik und magnetischen Induction (Individual contributions to Theoretical Mathematical Physics, in particular to Electrodynamics and Hydrodynamics, Electrostatics and Magnetic induction) (Leipzig, 1893), iii-iv, 205-6.
5. Maxwell, James C., Elizabeth Garber, Stephen G. Brush, C. W. Francis Everitt. (1995). Maxwell on Heat and Statistical Mechanics: On "avoiding All Personal Enquiries of Molecules" (pgs. 255, 257). Lehigh University Press.
6. Wallace, Thomas P. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations from Ancient Greece to America (Carl Neumann, pgs. 59, 104-05). AuthorHouse.
7. (a) Helm, Georg. (1887). The Theory of Energy: Historical-Critical Development (Die Lehre von der Energie: Historisch-kritisch Entwickelt) (pg. 72). Leipzig.
(b) Rabinbach, Anson. (1990). The Human Motor - Energy, Fatigue, and the Origins of Modernity (pg. 71). Berkeley: University of California Press.
(c) Wallace, Thomas. (2009). Wealth, Energy, and Human Values: the Dynamics of Decaying Civilizations (Carl Neumann, pgs. 59, 104-05). Author House.
8. (a) Helm, Georg F. (1898). Die Energetik: Nach Ihrer Geschichtlichen Entwickelung (Energetics: Historical Development). Leipzig.
(b) Helm, Georg F. (2000). The Historical Development of Energetics (Carl Neumann: special differential sign, pg. 130). Kluwer Academic Press.

External links
● Carl Neumann – Wikipedia.
● Carl Gottfried Neumann – Mathematics genealogy Project.