In thermodynamics, Carl Gottfried Neumann (1832-1925) was a German mathematicial physicist noted for his 1875 Lectures on the Mechanical Theory of Heat in which he introduction of the now-standard symbol notation đ (d-hat) or δ 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]

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]

References
1. (a) Neumann, Carl. (1875). Lectures on the Mechanical Theory of Heat (Vorlesungen über die mechanische Theorie der Wärme), Germany.
(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.

External links
● Carl Neumann – Wikipedia.