|A cartoon of a Szilard demon (information energy version of Maxwell demon), from the 1967 book Order and Chaos, with a negentropy flashlight, from which the demon obtains information about the movement and positions of the molecules in the room beyond the door (see also: Heisenberg uncertainty principle). |
In 1943, Erwin Schrodinger, gave his famous “What is Life?” lecture, wherein he famous posited that life is something that feeds on negative entropy. In the followup, Note to Chapter 6, in the 1944 book version of the lecture, Schrodinger clarified the following:
“Entropy taken with a negative sign is not my invention.”
In other words, that “–S” was something that predated 1943, whatever one wants to call it.
In 1950, French-born American physicist Leon Brillouin, in his article “Thermodynamics and Information Theory”, stated the following—his brackets and italics: 
“Every observation in the laboratory requires degradation of energy of energy and is made at the expense of a certain amount of negative entropy (abbreviation: negentropy), taken away from the surroundings.”
This seems to be the so-called “coining” of the now infamous silly term “negentropy” (the silliness is comparable to akin hypothetical terms: “negenergy” (negative energy) or “negheat” (negative heat), which we do not find in usage, because the ignorance is more obvious. Brillouin, in the preface to his 1956 book Science and Information Theory, specifically states that he "coined the word negentropy", which seems to be a reference to the above.
Into the 1950s, the term negentropy had gained a certain level of popularity. By 1956, owing to the work of Claude Shannon and Schrödinger, French physicist Léon Brillouin, for instance, in his book Science and Information Theory, had stated that “a new scientific theory has been born during the last few years, the theory of information.”  The basics of this theory, according to Brillouin, revolve around the question of how one is able to define the quantity of information communicated by a system of telegraph signals, signals which themselves consist of either electromagnetic or current transmissions. In this theory, the basic definition of information in a given operation, a quantity that Brillouin supposedly proves is “very closely related to the physical entropy of thermodynamics”, is defined by him as:
I = K ln P
where I denotes information, K is a constant, and P is the probability of the outcome. Brillouin reasons that with these types of probability arguments, “it enables one to solve the problem of Maxwell’s demon and to show a very direct connection between information and entropy” and that “the thermodynamic entropy measures the lack of information about a physical system.” Moreover, according to Brillouin, “whenever an experiment is performed in the laboratory, it is paid for by an increase in entropy, and a generalized Carnot principle states that the price paid in increase of entropy must always be larger than the amount of information gained.” Information, according to Brillouin, corresponds to “negative entropy” or negentropy, a term he coined.
In sum, Brillouin unjustifiably declares that the “generalized Carnot principle (second law) may also be called the negentropy principle of information”.
The origin of the so-called "negative entropy flashlight" seems to have originated in footnote eleven of Leon Brillouin’s 1949 article “Life, Thermodynamics, and Cybernetics” where in comment on American mathematician Norbert Wiener’s 1948 Cybernetics discussion of Maxwell’s demon comments: 
“One remark should be added. In order to choose the fast molecules, the demon should be able to see them; but he is in an enclosure in equilibrium at constant temperature, where the radiation must be that of the black body, and it is impossible to see anything in the interior of a black body. The demon simply does not see the particles, unless we equip him with a torchlight, and a torchlight is obviously a sours of radiation not at equilibrium. It pours negative entropy into the system.”
At this point, Brillouin is not yet using the term "negentropy" (short for negative entropy).
In 1971, American engineer Myron Tribus commented, in retrospect, that the demon was finally "exorcised" in 1951 by Brillouin who pointed out that if the demon were to identify the molecules, he would have to illuminate them in some way, causing an increase in entropy that would more than compensate for any decrease in entropy such a being could effect. 
The concept of negentropy stems from Léon Brillouin’s extended efforts to make a crossover information-thermodynamics science, a blend of the two of sorts. In his derivation, on the analogy of Helmholtz’s 1882 description “free energy” (available energy) and “bound energy” (entropy) of physical systems, Brillouin divides information into two classes: (a) free information, which occurs when the possible cases are regarded as abstract and have no specified physical significance, and (b) bound information, which occurs when the possible cases can be interpreted as complexions of a physical system. He states that bound information is a special case of free information.
Next, skipping a few point on probability arguments on the relation between entropy, information obtained, and numbers of complexions (as defined by Planck), Brillouin states that “bound information appears as a negative term in the total entropy of the physical system”, and we can conclude that:
Bound information Ib = decrease in entropy S= increase in negentropy N
where, as he states, we define negentropy as the negative of entropy and that “this statement represents the negentropy principle of information.” 
Difficulties on term | Objections to use
Well into the 1960s, the term generally found little objection. Statements can be found such as: 
“A fully living system must be capable of energy conversion in such a way as to accumulate negentropy, that is, it must produce a less probable, less random organization of matter and must cause the increase of available energy in the local system rather than the decrease demanded in closed systems by the second law of thermodynamics.”
After 1980, however, the term negentropy has been generally considered as a sloppy cross-over analogy and not recommenced for use in either information theory or in the study of the thermodynamics of living systems.  American chemical engineer Linus Pauling stated the point as "life does not feed on negentropy as a cat laps up milk."  American author Hubert Yockey has gone so far as to state that "the notion of negentropy has crept into the textbooks and the technical and popular literature" and that "it must be exorcised to avoid more damage". 
In 1994, Russian scientist Mikhail Bushev cogently explains that the term “negentropy” adds little if anything to the discussion: 
“Leon Brillouin gave this negative entropy the name negentropy and identified it with the information received by the system. The new term, however, does not contribute any new insight, neither into entropy, nor into information. The difference in the signs of these two quantities is similar to the difference between conveyed and received heat, conveyed and received work, etc.”
In other words, negentropy has about the same significance as if one were to introduce the term “negwork”, short for “negative work”, into the vernacular of science. The effect, in this hypothetical example, as we see, only acts to add a layer of confusion to a relatively straightforward situation.
A 1942 mention of the term "negentropy" is attributed to American physicist Robert Lindsay, supposedly by Dick Hammond, in reference to a type of ethics based on reducing entropy to the minimum or, in other words, increasing negentropy to the maximum.  In this sense, this would be the inverse of the metaphorical association of death with the state of maximum entropy, such that life would be associated with minimum entropy or a maximum negentropy principle. The actual "1942" Lindsay citation of negentropy terminology usage, however, may be missattribution. (Ѻ)
1. (a) Brillouin, Leon. (1950). “Thermodynamics and Information Theory” (abs), American Scientist, 38(4): 594-. Oct.; in: Modern Systems Research for the Behavioral Scientist: a Sourcebook (editor: Walter Buckley) (pgs. 161-65). Aldine Pub. Co., 1968.
(b) Brillouin, Léon. (1953). "Negentropy Principle of Information", J. of Applied Physics, v. 24:9, pp. 1152-1163.
(c) Brillouin, Léon. (1953). Science and Information Theory, (ch. 12: "Negentropy Principle of Information", pgs. 152-161). New York: Dover.
2. Perrot, Pierre. (1998). A to Z of Thermodynamics, Oxford: Oxford University Press.
3. (a) Negentropy - Web Dictionary of Cybernetics and Systems.
(b) Yockey, Hubert P. (2005). Information Theory, Evolution, and the Origin of Life, (pg. 32). Cambridge: Cambridge University Press.
4. Pauling, Linus. (1987). “Schrödinger's contribution to chemistry and biology”, in: Schrödinger: Centenary of a Polymath. Cambridge, UK: Cambridge University Press.
5. Yockey, Hubert P. (2005). Information Theory, Evolution, and the Origin of Life (pg. 32). Cambridge University Press.
6. Simpson, G. G. (1964). "The Nonprevalence of Humanoids", Science, 143: 769-75.
7. Brillouin, Léon. (1956). Science and Information Theory (ch. 12: "Negentropy Principle of Information", pgs. 152-161). New York: Dover.
8. Angrist, Stanley, W. and Helpler, Loren G. Order and Chaos - Laws of Energy and Entropy, (pg. 196-214). New York: Basic Books.
9. (a) Page reference in the 1942 issue of Sigma Xi Quarterly.
(b) Hammond, Dick K. (2005). The Human System from Entropy to Ethics (pgs. 12-14). Publisher: Dick Hammond.
(c) Lindsay, Robert. (1942). “The Impact of Science on Contemporary Civilization” (Ѻ), Sigma Xi Quarterly: v.30, no. 1.
10. Brillouin, Leon. (1949). “Life, Thermodynamics, and Cybernetics” (footnote 11) (abs), American Scientist, Vol. 37, pgs. 554-68; In: Biology and Computation: a Physicist’s Choice (pgs. 37-51), by H. Gutfreudn and G. Toulouse. World Scientific, 1994; In: Maxwell’s Demon 2: Entropy, Classical and Quantum Information, Computing (pgs. 73-87), Harvey S. Leff, Andrew F. Rex. CRC Press, 2003.
11. Tribus, Myron and McIrving, Edward C. (1971). “Energy and Information”, Scientific American, 225: 179-88.
12. Bushev, Mikhail. (1994). Synergetics: Chaos, Order, and Self-Organization (pg. 247). World Scientific.
● Popper, Karl R. (1967). “Time’s Arrow and Feeding on Negentropy”, Nature, 213 (5079): 320-.
● Woolhous, H. W. (1967). “Negentropy Information and Feeding on Organisms”, Nature 213 (5079): 952+.
● Mae-Wan Ho. (1994). What is (Schrödinger's) Negentropy?, Modern Trends in BioThermoKinetics 3, 50-61.
● Negentropica - an e-Journal on negentropy, thermodynamics, and self-organized phenomena (2001-2003).
● Negentropy – Wikipedia.