In science, struggle for entropy is an enigmatic postulate, stated by Austrian physicist Ludwig Boltzmann in 1886, which argues that life is not a struggle for energy or food but rather for entropy (or for free energy, depending on translation?) [1]

Boltzmann | struggle for free energy?
The specific famous quote where Boltzmann's explains Charles Darwin's 1859 "struggle for existence" theory of evolution in thermodynamics terms is said to be found in his 1886 article “The Second Law of Thermodynamics” (“Der Zweite Hauptsatz der Mechanischen Warmetheorie”). The English translations for this explanation, however, are wanting, differing on a number of points, and come in a variety of forms.

In 1893, German chemist Walther Nernst supposedly gave the following version (according to the 1895 English translation by American chemist Charles Palmer): [7]

“Strife is not for the component substances, for these component substances of all organism, as air, water, and earth, are abundant; neither is the strife for energy as such, for this occurs in abundance, as the heat content of matter of our environment; but strife is for the free energy available for the performance of work.”

In 1942, American Gibbsian historian Muriel Rukeyser stated that Boltzmann said the following: [8]

“The struggle for existence of living matter is a war for free energy.”

Boltzmann | struggle for entropy?
Into the 21st century, somehow the quote was being translated in English as "struggle for entropy". In 2005, for example, Eric Schneider gave the following paragraph as the standard English translation:

“The general struggle for existence of animate beings is not a struggle for raw materials – these, for organisms, are air, water and soil, all abundantly available – nor for energy, which exists in plenty in any body in the form of heat Q, but of a struggle for entropy, which becomes available through the transition of energy from the hot sun to the cold earth.”

but then goes onto state that Alfred Lotka cited Boltzmann as saying that life is a struggle for "available entropy" and that in modern terms, according to Schneider, the translation reads that life is a struggle for "available energy". [9]

In his high-cited 1971 The Entropy Law, Romanian mathematician Nicholas Georgescu-Roegen commented that: [3]

“Life does not feed on mere matter and mere energy but—as Schrodinger aptly explained—on low entropy. The seed of this idea goes back to Ludwig Boltzmann who was the first to point out that free energy is the object of the struggle for life. ”

This, to clarify, is pure mis-quote. It seems that Georgescu-Roegen, who had an very incorrect understanding of free energy, substituted the term “free energy” for “entropy”. The actual term “free energy”, to note, was only coined four years earlier, in 1882, by German physicist Hermann Helmholtz in the field of chemical thermodynamics (Boltzmann's field was statistical thermodynamics). It is highly unlikely that Boltzmann had even heard this term at this time, let alone feel confident enough to assign it as the object of the struggle of life. This “free energy is the object of the struggle for life” Boltzmann mis-quote, subsequently, has frequently been re-quoted since, as shown below:


Left: The 1982/2000 footnoted misquote of Boltzmann, via Georgescu-Roegen, by Italian architect Luis Fernández-Galiano. [5] Right: The 1993 footnoted misquote of Boltzmann, via Georgescu-Roegen, by English cultural historian Thomas Richards. [6]

To clarify, entropy, symbol S:

$S = \frac{Q}{T} \,$

and free energy, either of the Helmholtz free energy (isothermal-isochoric), symbol H variety:

$H = U - TS \,$

or the Gibbs free energy (isothemal-isobaric) symbol G variety:

$G = U + p V - T S\,$

are two hugely different thermodynamic functions. The point to note here, commonly found in outside field verbal explanations of thermodynamics (e.g. entropology), is that lack of understanding of topic can result in perpetual unintentional spread of misinformation. An example of this being Shannon information theory.

Schrodinger
Boltzmann's view was expanded on in Austrian physicist Erwin Schrodinger's 1944 What is Life?, wherein Schrodinger outlined the view, using crude probability arguments, that: “[Life] feeds on negative entropy.” The basic difficulty in Schrödinger’s negative entropy theory is that he equates sustenance (metabolism) with measures of entropy; whereas in the correct sense, sustenance is a function of substrate interactions, as studied in the field of surface chemistry. In an appended note to his thermodynamics-life chapter, however, Schrödinger states that:

“The remarks on negative entropy have met with doubt and opposition from physicist colleagues. Let me say first, that if I had been catering for them alone I should have let the discussion turn on free energy instead. It is the more familiar notion in this context. But this highly technical term seemed linguistically too near to energy for making the average reader alive to the contrast between the two things.”

References
1. Boltzmann, Ludwig. (1886). The Second Law of Thermodynamics (pgs. 14-32; struggle quote, pg. 24, affinity and energy set free, pgs. 26-27). In B. McGinness, ed., Ludwig Boltzmann: Theoretical physics and philosophical problems: Select Writings. Dordrecht, Netherlands: D. Reidel, 1974.
2. (a) Schrödinger, Erwin. (1944). What is Life? (ch. 6 “Order, Disorder, and Entropy). pgs. 67-75. Cambridge: Cambridge University Press.
(b) What is Life? (1944 book in word doc download).
3. (a) Georgescu-Roegen, Nicholas. (1966). Analytical Economics: Issues and Problems (pg. 82). Harvard University Press.
(b) Georgescu-Roegen, Nicholas. (1971). The Entropy Law and the Economic Process (pg. 192). Cambridge, Massachusetts: Harvard University Press.
4. Boltzmann, Ludwig. (1886). “Der Zweite Hauptsatz der Mechanischen Warmetheorie (The Second Law of the Mechanical Theory of Heat.” Popular Schriften, pgs. 25-50.
5. Fernández-Galiano, Luis and Carino, Gina (translator) (2000). Fire and Memory: On Architecture and Energy (originally written in 1982) (pg. 277). MIT Press.
6. Richards, Thomas. (1993). The Imperial Archive: Knowledge and the Fantasy of Empire (pg. 94). Verso.
7. (a) Nernst, Walther. (1895). Theoretical Chemistry: from the Standpoint of Avogadro’s Rule & Thermodynamics (Book III, ch. VII: Photo-Chemistry, pgs. 617-; section: Theory of Photo-Chemical Action, pgs. 626-28). MacMillan and Co.
(b) Boltzmann, Ludwig. (1886). “Der Zweite Hauptsaz der Mech. Warmeth. (The Second Law of Thermodynamics), pg. 21. Vortrag., Wien bei.
8. Rukeyser, Muriel. (1942). Willard Gibbs - American Genius (pg. 314-15). Garden City, New York: Doubleday, Doran & Co., Inc.
9. Schneider, Eric D. and Sagan, Dorion. (2005). Into the Cool - Energy Flow, Thermodynamics, and Life (struggle for life, pgs. 60, 147, 150), . Chicago: The University of Chicago Press.