Social ideal gas law

Ideal gasvacuum bulb (1663)
Left: a generic model idealization of an ideal gas in a frictionless piston and cylinder. Right: A 1663 vacuum pump (bottom part), showing the vacuum bulb (top part), the third design of the vacuum pump by German engineer Otto Guericke, the prototype behind Robert Boyle's pneumatical engine, through which Boyle's law was arrived at, and, in turn, the other various gas laws, culminating in the ideal gas law. Both being models used by hmolscience scholars into the 20th century to model society. A more accurate model is the van't Hoff equilibrium box, such as discussed in American chemical thermodynamicist Frederick Rossini's famous 1971 "Chemical Thermodynamics in the Real World".
In hmolscience, social ideal gas law, "human gas law", "social gas law", or "social equation of state", etc., refers to attempts to formulate models of human society based on one of the gas laws or the ideal gas law.

Overview
A number of individuals to have attempted human, human molecule, human particle, or sociological equivalent extrapolations of the classical "ideal gas law" as models of human behavior, in the form of a "human ideal gas law" or "social ideal gas law".

In 1925, Alfred Lotka, in his Elements of Physical Biology (pg. 305), did a rather cogent social ideal gas law derivation.

In 1947, American physicist John Q. Stewart, in his “Suggested Principles of ‘Social Physics’”, attempted to outline, formulaically, what he called a “human gas” model of population demographics, in which he viewed each person as a “molecule” (or human molecule, in the modern sense of the term) and used the following shorthand version of ideal gas law:

 pa = NT \,

where p is "demographic pressure", a is an area of land occupied by N individuals (human molecules), and T is the "demographic temperature", combined with population census data, to derive concepts such as “demographic energy”, "demographic force", and “demographic gravitation”, among others. [1]

In 1952, English physicist C.G. Darwin, in his "Introduction" chapter to his The Next Million Years, stated the following:

“We ought to be able to foresee the general character of the future history of mankind. The operation of the laws of probability should tend to produce something like certainty. 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.”
C.G. Darwin (1952), “Introduction” to The Next Million Years

He then employed Boyle's law:

PV = K\mid_{n,T} \,

to introduce the subject of the statistical mechanical study of conservative dynamical systems of human molecules or the science of "human thermodynamics" as he called it.

In 1970, Paul Samuelson, in his Nobel Prize speech “Maximum Principles in Analytical Economics”, as cited by John Bryant during BPE 2016, described his use of a variant of Boyle's law in economics as follows: [4]

“I was struck by a remark made by an old teacher of mine at Harvard, Edwin Bidwell Wilson. Wilson was the last student of J. Willard Gibbs' at Yale and had worked creatively in many fields of mathematics and physics; his advanced calculus was a standard text for decades; his was the definitive write-up of Gibbs' lectures on vectors; he wrote one of the earliest texts on aerodynamics; he was a friend of R. A. Fisher and an expert on mathematical statistics and demography; finally, he had become interested early in the work of Pareto and gave lectures in mathematical economics at Harvard. My earlier formulation of the inequality in Eq. 4:

eq. 4 (Samuelson)

owed much to Wilson's lectures on thermodynamics. In particular, I was struck by his statement that the fact that an increase in pressure is accompanied by a decrease in volume is not so much a theorem about a thermodynamic equilibrium system as it is a mathematical theorem about surfaces that are concave from below or about negative definite quadratic forms. Armed with this clue, I set out to make sense of the Le Chatelier principle.”

In 2009, Hungarian gender studies scholar Agnes Kovacs, in conference presentations, and in 2012, in her “Gender Studies in the Substance of Chemistry”, used the ideal gas law to outline what she called “feminist chemical thermodynamics.” [3]

Other usages of the ideal gas law as a basis to formulate economic and social theory include John Bryant (2009) and Mohsen Mohsen-Nia (2013), respectively. [2]

References
1. Stewart, John Q. (1947). “Suggested Principles of ‘Social Physics’”, Science, 106(2748):179-80, Aug 29.
2. (a) Bryant, John (2009). Thermoeconomics: A Thermodynamic Approach to Economics (ch. 1: Introduction; ch. 3: Thermodynamic Principles; ch. 5: Money). VOCAT International Ltd.
(b) Mohsen-Nia, Mohsen. (2013). “Social Equation of State”, Journal of Human Thermodynamics, in Review (Apr 30-).
3. (a) Kovacs, Agnes. (2012). “Gender Studies in the Substance of Chemistry, Part 1: The Ideal Gas Law”, Hyle: International Journal for Philosophy of Chemistry, 18 (2), 95-120.
(b) Kovacs, Agnes. (2012). “Gender in the Substance of Chemistry, Part 2: An Agenda for Theory”, Hyle: International Journal for Philosophy of Chemistry, 18 (2), 121-43.
(c) Agnes Melinda Kovacs (faculty) – Central European University.
4. (a) Samuelson, Paul A. (1970). “Maximum Principles in Analytical Economics” (pgs. 67-68), Nobel Prize Lecture; in: Science, 173(1971):993-94.
(b) Hunsaker, Jerome and Mac Lane, Saunders. (1973). “Edwin Bidwell Wilson (1879-1964)” (pdf) (pgs. 297-98), 38-pages. National Academy of Sciences.

Further reading
‚óŹ Potter, Elizabeth. (2001). Gender and Boyle’s Law of Gases. Indiana University Press.

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