|American physicist Wayne Saslow's 1999 thermodynamic analogies, i.e. so-labeled "analogies" between thermodynamic and economic systems; one of many historical human thermodynamic variables table, which date back to American economist Irving Fisher (1892). |
Discussion | Analogy vs Reality
In the late 19th century, thermodynamic analogies began to accumulate, most implicit, some explicitly, stated as "analogies" as a matter of discourse.
The subject itself is a rather involved an intricate one, being that by the turn of the early 20th century, the first and second law were proved to govern and to apply to "every" system in the universe, without exception; hence when one says, e.g. that the "energy of the processes occurring in a given social system is conserved" this is not analogy but fact. If, conversely, we say, e.g., that the "energy of money is conserved" or that, as William Ramsay (1898) said, the collisions of gas molecules are like the collisions of football players, these are what are called a gray area analogies, some more accurate than others and many completely off-base or incorrect and some real or not analogy; take, e.g. the following statement on Frederick Rossini's 1971 "Chemical Thermodynamics in the Real World" assertion and followup Rossini debate:
“A well-drawn analogy between two surprisingly dissimilar concepts can not only be helpful in the classroom, it can be pleasing and instructive on its own merits, as long as one is cognizant of its limitations. On the surface, Rossini’s analogy relating enthalpy, entropy, and the equilibrium constant to freedom and security in the modern nation-state seems like a good example of an unusual and instructive comparison. I was initially intrigued. Using the thermodynamic conclusion that (a) a reaction’s spontaneity (or Keq) increases when either ∆H gets more negative (stronger security) or ∆S gets more positive (more freedom), Rossini analogized that (b) “One cannot have a maximum of freedom and a maximum of security at the same time.” Sadly, point (a), although true, does not support point (b), not even in the limited realm of chemical thermodynamics, much less in the broader realm of political governance.”— Todd Silverstein (2006), “State Functions vs State Governments”, Jun 
Here we see confusion, namely: Rossini presented his lecture as a real world non-analogy application, whereas Silverstein re-interpreted his argument as "analogy".
The Moriarty-Thims debate (2009) centered around whether an ordering of students has a "thermodynamic" entropy, in reality, NO analogy, or whether the teaching heuristic of referring to people grouped in a field, as compared to scattered randomly, is but "analogy" and in reality they ordering of students have no measurable entropy.
The following, to give a comparison example, done by Brazilian chemical engineer Jaime Aguilar-Arias (2014), between the so-labeled "Mohsen analogies", made by American chemical engineer Mohsen Mohsen-Nia (2013), and the "Bryant analogies", made by English mechanical engineer John Bryant (2011): 
Here, we see temperature, assigned by seeming analogical guess, to "motivation in society" (Mohsen, 2013) and "index of trading value" (Bryant, 2011); prolonged discussion would be requisite to discern which analogy, in regard to this variable, is more exact (truer) or correct (or incorrect).
Historical | Examples
In 1952, English physicist C.G. Darwin, to give another example, defined "human thermodynamics" as the "thermodynamic study of systems of human molecules", in his book in his The Next Million Years, wherein he used the word 'analogy' 19-times, comparing humans, by analogy, to the molecules of a body of gas governed by Boyle's law, to the behavior of a wild animal, and to the behavior of ants. The following are few representative quotes:
“The analogy I have cited of the gas laws is the simplest example that is furnished by statistical mechanics, and it is only fair to mention that, when the subject is pursued further, it does get a good deal more complicated. Thus much greater difficulties arise in considering how the gas can condense into a liquid or solid, but it would not be profitable to follow the analogy into these intricacies. We may, so to speak, reasonably hope to find the Boyle's Law which controls the behavior of those very complicated molecules, the members of the human race, and from this we should be able to predict something of man's future. The possibility depends on finding out whether there are for humanity any similar internal conditions, which would be analogous to the condition of being a conservative dynamical system, and external conditions analogous to the containing vessel.
In the gas, the external conditions were given by the containing vessel, and the analogy here is obviously the earth itself. The internal principle, which is to be analogous to the property of being conservative dynamical systems, of course lies deeper. It must depend on the laws governing the nature and behaviour of the human molecules. When I compare human beings to molecules, the reader may feel that this is a bad analogy, because unlike a molecule, a man has free will, which makes his actions unpredictable. Though the individual collisions of the human molecules may be a little less predictable than those of gas molecules—which, as I have said, do not have to be considered in detail either—the census returns show that for a large population the results average out with great accuracy. The internal principle then of the human molecules is human nature itself. On the analogy between human history and the molecules of a gas, the different civilizations are to be ranked as fluctuations from the average.”
In objection to this definition, many argue, on what seem to be emotional, religious, or philosophical grounds, that this statement is pure analogy.
In 1997, Swedish physical chemist Sture Nordholm published his famous “In Defense of Thermodynamics: an Animate Analogy”, wherein he gives rather well-honed advice and rules of thumb when attempting to formulate thermodynamic analogies, namely that it is a matter of "proper translation", or in more detail:
“The purity and precision of thermodynamics has been maintained on the strength of its validity only as a collection of limiting laws for infinitely large systems undergoing infinitely slow changes. However, the interest in thermodynamics has always been based on the great relevance for finite real systems undergoing changes that are fast on our everyday time scale and slow only on the microscopic time scale of atomic motion. Thus we are merely extending the beam of insight from the lifeless behaviors of inanimate matter to the vivid complexities of human behavior. In the final analysis this far-reaching analogy rests on the fact that the basic elements of the description of atoms, molecules, and matter can be scaled up to the realm of living organisms without changes other than in the complexity of the systems and their behavior.”
In 2006, Polish science-philosopher theologian Jozef Zycinski stated that in his 2000 article “God, Freedom, and Evil: Perspectives from Religion and Science” he “offers an interpretation of human behavior with consideration of analogies from thermodynamics”. 
In 2008, American physical chemist Thomas Wallace argued that the rise and fall of civilizations can be explained thermodynamically on the analogy of the five-year operational life of a car battery. 
In 2013, Jason Smith, in his “Economics for Fun and Profit”, spent time blogging on thermodynamic analogies, and how Paul Samuelson (1960) objected to them; to quote a snippet: 
“Oh snap. Anyway, some of the basic ideas that came out of the thermodynamic analogy seem to be that goods are extensive measures like energy or volume and prices are intensive measures like pressure or temperature. Hey, that's what I found! Prices are like pressure, the quantity supplied is like volume and the quantity demanded is like energy in the information transfer model.”
The following are related quotes:
“The formal mathematical analogy between classicalthermodynamics and mathematical economic systems has nowbeen explored. This does not warrant the commonly metattempt to find more exact analogies of physical magnitudes—such as entropy or energy—in the economic realm. Whyshould there be laws like the first or second laws ofthermodynamics holding in the economic realm? Why should "utility'' be literally identified with entropy, energy, or anythingelse? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematicalisomorphism that does exist between minimum systems thatarise in different disciplines?”— Paul Samuelson (1960), "Publication"; cited by Jason Smith 
“This is all just a horrendous analogy. Chemical laws apply to humans, but our behavior is more complex than something that can be modeled with a couple of thermodynamic equations. A + B → AB is just a pretentious way of stating something we already know; it tells us absolutely nothing new.”— Ryan Grannell (2011), “Category: Human Chemistry” 
● Black cat analogy
● Chemical analogy
● Exact analogy
● Mathematical analogy
● Physical analogy
1. Saslow, Wayne M. (1999). “An Economic Analogy to Thermodynamics”, Am. J. Phys. 67(12): 1239-47.
2. (a) Smith, Jason. (2013). “Economics for Fun and Profit” (Ѻ), Information Transfer Economics, BlogSpot, Apr 1.
(b) Smith, Jason. (2013). “Are the Thermodynamic Analogies Useful?” (Ѻ), Information Transfer Economics, BlogSpot, Apr 27.
3. Aguilar-Arias, Jaime L. (2014). “Chemical Engineering and Complexity, an Undissipated Structure … Yet”, 20th Brazilian Congress of Chemical Engineering (Congresso Brasilerro de Enenharia Quimica, XX) (pdf), Florianopolis, Brazil, Oct 19-22.
4. Silverstein, Todd, P. (2006). “State Functions vs. State Governments”, Journal of Chemical Education, Jun. (83): 847, Letters.
5. Grannell, Ryan. (2011). “Category: Human Chemistry”, Bag of Many Things, WordPress.com (Jun 26 –Jul 22).
● Lindsay, Robert B. (1963). The Role of Science in Civilization, (section: "Information Theory and Thermodynamics: Entropy", pgs. 153-65; section: "A Scientific Analogy: The Thermodynamic Imperative", pgs. 290-98). Westport: Greenwood Press. Dowden, Hutchinson & Ross.