In science, neo-vitalism are versions of vitalism promoted or theorized about in the post Helmholtz school formation years, 1842 or thereafter, or thereabouts, in to the 1920s, approximately.

Overview
In 1842, the Reymond-Brucke oath was penned and signed in blood, so the legend has it: [1]

“[We pledge] to put in power this truth: no other forces than the common physical chemical ones are active within the organism. In those cases which cannot at the time be explained by these forces one has either to find a specific way or form of their action by means of physical mathematical method, or to assume new forces equal in dignity to the chemical physical forces inherent in matter, reducible to the force of attraction and repulsion.”

Neo-vitalism, in other words, are types of vitalism beyond that of the classical Johannes Muller model of vitalism.

In 1894, French-German science translator Frances A. Welby, in his article “Neo-Vitalism”, gave the following historical: [2]

“A Quarter of a century ago, du Bois-Reymond headed the revolt of mechanicalist biology against the vitalism of Johannes Müller. From Bichat to Magendie, from Johannes Müller to Schwann, the pendulum swung backwards and forwards; but it was reserved for du Bois-Reymond, in his now famous Berlin addresses, together with Ludwig and Helmholtz, to expose the fallacies of vitalism, and establish physiology on a mechanical basis.”

In 1921, English biologist (chnopsologist) James Johnstone, in his chapter on the nature of life, stated: [3]

“Into the last generation there has been a recrudescence of vitalism—‘neo-vitalism’ it is now called—being obviously something that seems to be different from the Cartesian speculations about the sensitive soul. At its best this is seen in the ‘psychoids’ and ‘entelechies’ of Driesch and others, concepts which are applicable to living things only, and not to chemical and physical phenomena. At its worst modern vitalism is exhibited in the crude and even grotesque ‘spiritualism’ which has attained such a vogue with the less resolute thinkers of our own generation. This, then, is the modern impasse to which biology has come. Purely physico-chemical explanations of life are not satisfactory, and the immaterial and non-energetic agencies that are being invoked in their place have no interest for science, since they cannot be the objects of investigations.”

in the last sentence of Johnstone's book, he states: “life probably itself has existed on earth for 1,000 million years [and] in living processes the increase of entropy is retarded—this is our ‘vital’ concept.” This is a type of “physics-disguised vitalism”, which is difficult to pin down, often requiring that one is an expert in a number of fields so as to be able to pin down the underlying vitalism or neo-vitalism. Here, in short, Johnstone is invoking a contrived thermodynamic argument, i.e. entropy reversal (or entropy reduction), to salvage the view that certain types of matter can be considered alive.

In 1966, Francis Crick, in the wake of 1963 vitalism debates, with so-called metaphysical vitalism of Pierre Teilhard and the scientific vitalism of Michael Polanyi, among others, e.g. Walter Elsasser, penned his Molecules and Men, wherein he stated the following: [4]

Neo-vitalists [are those] who hold vitalistic ideas but do not want to be called a vitalist.”

Crick went on to state suggest: "we should abandon the word 'alive'." This was one of the stepping stones to the defunct theory of life.

References
1. Murray, Henry A. and White, Robert W. (2006). The Study of Lives: Essays on Personality in Honor of Henry A. Murray (pg. 372-75). Aldine Transaction.
2. Welbey, Frances A. (1894). “Neo-Vitalism” (abs), Nature, 51:43-44.
3. Johnstone, James. (1921). The Mechanism of Life in Relation to Modern Physical Theory (pg. 159, 193). Longmans, Green & Co.
4. Crick, Francis. (1966). Of Molecules and Men (pg. #). University of Washington Press.

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