Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910 American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of thermodynamics and on the principle of entropy.Adams, Henry. (1986). History of the United States of America During the Administration of Thomas Jefferson (pg. 1299). Library of America.Adams, Henry. (1910). A Letter to American Teachers of History. Google Books, Scanned PDF. Washington.

The 1944 book What is Life? by Nobel-laureate physicist Erwin Schrödinger stimulated further research in the field. In his book, Schrödinger originally stated that life feeds on negative entropy, or negentropy as it is sometimes called, but in a later edition corrected himself in response to complaints and stated that the true source is free energy. More recent work has restricted the discussion to Gibbs free energy because biological processes on Earth normally occur at a constant temperature and pressure, such as in the atmosphere or at the bottom of the ocean, but not across both over short periods of time for individual organisms. The quantitative application of entropy balances and Gibbs energy considerations to individual cells is one of the underlying principles of growth and metabolism.

Ideas about the relationship between entropy and living organisms have inspired hypotheses and speculations in many contexts, including psychology, information theory, the origin of life, and the possibility of extraterrestrial life.

Early views In 1863 Rudolf Clausius published his noted memoir On the Concentration of Rays of Heat and Light, and on the Limits of Its Action, wherein he outlined a preliminary relationship, based on his own work and that of William Thomson (Lord Kelvin), between living processes and his newly developed concept of entropy. Building on this, one of the first to speculate on a possible thermodynamic perspective of organic evolution was the Austrian physicist Ludwig Boltzmann. In 1875, building on the works of Clausius and Kelvin, Boltzmann reasoned:

In 1876 American civil engineer Richard Sears McCulloh, in his Treatise on the Mechanical Theory of Heat and its Application to the Steam-Engine, which was an early thermodynamics textbook, states, after speaking about the laws of the physical world, that "there are none that are established on a firmer basis than the two general propositions of Joule and Carnot; which constitute the fundamental laws of our subject." McCulloh then goes on to show that these two laws may be combined in a single expression as follows:

where

entropy a differential amount of heat passed into a thermodynamic system absolute temperature

McCulloh then declares that the applications of these two laws, i.e. what are currently known as the first law of thermodynamics and the second law of thermodynamics, are innumerable:

McCulloh gives a few of what he calls the "more interesting examples" of the application of these laws in extent and utility. His first example is physiology, wherein he states that "the body of an animal, not less than a steamer, or a locomotive, is truly a heat engine, and the consumption of food in the one is precisely analogous to the burning of fuel in the other; in both, the chemical process is the same: that called combustion." He then incorporates a discussion of Antoine Lavoisier's theory of respiration with cycles of digestion, excretion, and perspiration, but then contradicts Lavoisier with recent findings, such as internal heat generated by friction, according to the new theory of heat, which, according to McCulloh, states that the "heat of the body generally and uniformly is diffused instead of being concentrated in the chest". McCulloh then gives an example of the second law, where he states that friction, especially in the smaller blood vessels, must develop heat. Undoubtedly, some fraction of the heat generated by animals is produced in this way. He then asks: "but whence the expenditure of energy causing that friction, and which must be itself accounted for?"

To answer this question he turns to the mechanical theory of heat and goes on to loosely outline how the heart is what he calls a "force-pump", which receives blood and sends it to every part of the body, as discovered by William Harvey, and which "acts like the piston of an engine and is dependent upon and consequently due to the cycle of nutrition and excretion which sustains physical or organic life". It is likely that McCulloh modeled parts of this argument on that of the famous Carnot cycle. In conclusion, he summarizes his first and second law argument as such:

Negative entropy In the 1944 book What is Life?, Austrian physicist Erwin Schrödinger, who in 1933 had won the Nobel Prize in Physics, theorized that life – contrary to the general tendency dictated by the second law of thermodynamics, which states that the entropy of an isolated system tends to increase – decreases or keeps constant its entropy by feeding on negative entropy. The problem of organization in living systems increasing despite the second law is known as the Schrödinger paradox. In his note to Chapter 6 of What is Life?, however, Schrödinger remarks on his usage of the term negative entropy:

This, Schrödinger argues, is what differentiates life from other forms of the organization of matter. In this direction, although life's dynamics may be argued to go against the tendency of the second law, life does not in any way conflict with or invalidate this law, because the principle that entropy can only increase or remain constant applies only to a closed system which is adiabatically isolated, meaning no heat can enter or leave, and the physical and chemical processes which make life possible do not occur in adiabatic isolation, i.e. living systems are open systems. Whenever a system can exchange either heat or matter with its environment, an entropy decrease of that system is entirely compatible with the second law.The common justification for this argument, for example, according to renowned chemical engineer Kenneth Denbigh in his 1955 book The Principles of Chemical Equilibrium, is that "living organisms are open to their environment and can build up at the expense of foodstuffs which they take in and degrade."

Schrödinger asked the question: "How does the living organism avoid decay?" The obvious answer is: "By eating, drinking, breathing and (in the case of plants) assimilating." While energy from nutrients is necessary to sustain an organism's order, Schrödinger also presciently postulated the existence of other molecules equally necessary for creating the order observed in living organisms: "An organism's astonishing gift of concentrating a stream of order on itself and thus escaping the decay into atomic chaos – of drinking orderliness from a suitable environment – seems to be connected with the presence of the aperiodic solids..." We now know that this "aperiodic" crystal is DNA, and that its irregular arrangement is a form of information. "The DNA in the cell nucleus contains the master copy of the software, in duplicate. This software seems to control by specifying an algorithm, or set of instructions, for creating and maintaining the entire organism containing the cell."Nelson, P. (2004). Biological Physics, Energy, Information, Life. W.H. Freeman and Company.

DNA and other macromolecules determine an organism's life cycle: birth, growth, maturity, decline, and death. Nutrition is necessary but not sufficient to account for growth in size, as genetics is the governing factor. At some point, virtually all organisms normally decline and die even while remaining in environments that contain sufficient nutrients to sustain life. The controlling factor must be internal and not nutrients or sunlight acting as causal exogenous variables. Organisms inherit the ability to create unique and complex biological structures; it is unlikely for those capabilities to be reinvented or to be taught to each generation. Therefore, DNA must be operative as the prime cause in this characteristic as well. Applying Boltzmann's perspective of the second law, the change of state from a more probable, less ordered, and higher entropy arrangement to one of less probability, more order, and lower entropy (as is seen in biological ordering) calls for a function like that known of DNA. DNA's apparent information-processing function provides a resolution of the Schrödinger paradox posed by life and the entropy requirement of the second law.Peterson, Jacob. "Understanding the Thermodynamics of Biological Order". The American Biology Teacher, 74, Number 1, January 2012, pp. 22–24.

Gibbs free energy and biological evolution In recent years, the thermodynamic interpretation of evolution in relation to entropy has begun to use the concept of the Gibbs free energy, rather than entropy.Higgs, P. G., & Pudritz, R. E. (2009). "A thermodynamic basis for prebiotic amino acid synthesis and the nature of the first genetic code" Accepted for publication in Astrobiology This is because biological processes on Earth take place at roughly constant temperature and pressure, a situation in which the Gibbs free energy is an especially useful way to express the second law of thermodynamics. The Gibbs free energy is given by:

where

Gibbs free energy enthalpy passed into a thermodynamic system absolute temperature of the system entropy

and exergy and Gibbs free energy are equivalent if the environment and system temperature are equivalent. Otherwise, Gibbs free energy will be less than the exergy (for systems with temperatures above ambient). The minimization of the Gibbs free energy is a form of the principle of minimum energy (minimum 'free' energy or exergy), which follows from the entropy maximization principle for closed systems. Moreover, the Gibbs free energy equation, in modified form, can be used for open systems, including situations where chemical potential terms are included in the energy balance equation. In a popular 1982 textbook, Principles of Biochemistry, noted American biochemist Albert Lehninger argued that the order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division. In short, according to Lehninger, "Living organisms preserve their internal order by taking from their surroundings free energy, in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy."

Similarly, according to the chemist John Avery, from his 2003 book Information Theory and Evolution, we find a presentation in which the phenomenon of life, including its origin and evolution, as well as human cultural evolution, has its basis in the background of thermodynamics, statistical mechanics, and information theory. The (apparent) paradox between the second law of thermodynamics and the high degree of order and complexity produced by living systems, according to Avery, has its resolution "in the information content of the Gibbs free energy that enters the biosphere from outside sources."