In human thermodynamics, Vilfredo Pareto (1848-1923) was a French-Italian mathematical engineer noted for his efforts to formulate a hard science version of sociology. In his own words: [5]

“My wish is to construct a system of sociology on the model of celestial mechanics, physics, and chemistry.”

Education
Pareto completed his BS in mathematical sciences in 1867 and his PhD engineering, in 1870, with a dissertation on "The Fundamental Principles of Equilibrium in Solid Bodies", both from what is now the Polytechnic University of Turin. It is said that his later interest in equilibrium analysis in economics and sociology can be traced back to his dissertation.

Overview
Pareto is generally known for his social thermodynamics and economic thermodynamics theories, as were outlined towards the end of the 19th century, on the logic of his mentor French economist Léon Walras, who had previously spoken and theorized about of people as "economic molecules".

Human molecules
It is said that Pareto specifically used the term "human molecule"; the source of this, however, remains to be be tracked down. The attributed quite, circa 1896, is:

“Society is a system of human molecules in a complex mutual relationship.”

In his in his 1896 Course of Political Economics, he states: [6]

“First we separate the study of ophelimity (economic satisfaction) from the diverse forms of utility, then we direct our attention to man himself; stripping him of a large number of his attributes, leaving out the passions, good or bad, reducing him to a kind of molecule that only acts in response to the forces of ophelimity.”

Likewise:

“Economic phenomena are not static, but dynamic. The molecules which combine to form the social aggregate are in constant motion. We may for the sake of analysis take certain average economic positions, as we take the average level of the ocean.”

Gibbs
It is often said that Pareto transposed his theory of social equilibria directly from the theory of chemical equilibria advanced by American mathematical physicist Willard Gibbs as found in his 1876 On the Equilibrium of Heterogeneous Substance, the founding paper of chemical thermodynamics. [7]

This view, however, seems to have been a supposition made by American physiologist Lawrence Henderson in the 1930s and thereafter taken as fact, but in reality does not seem to have occurred. It is doubtful that the Equilibrium work of Gibbs would have been known to Pareto in the 1890s. In fact the first non-English translations of Gibbs' 1876 Equilibrium were in German (1892) and French (1899).

In any event, Henderson argues that Pareto's 1916 Treatise on General Sociology, he attempted to construct a system of sociology analogous in its essential features to the generalized physico-chemical thermodynamics system as outlined in Gibbs' Equilibrium. [1]

Entropy
In his discussions and theories on mind and society, Pareto was cognizant of the concept of entropy but eschewed it, instead relying heavily upon the concept of equilibrium. [4]

Recent views
In the 2003 article “Money in Gas-Like Markets: Gibbs and Pareto Laws”, several authors consider ideal-gas models of trading markets, where each agent is identified with a gas molecule and each trading as an elastic or money-conserving (two-body) collision. Unlike in the ideal gas, they introduce a quantity the “saving propensity” $λ of agents, such that each agent saves a fraction $λ of its money and trades with the rest. They show that steady-state money or wealth distribution in a market is Gibbs-like for relation $λ = 0, has a non-vanishing most-probable value for $λ ≠ 0, and Pareto-like when $λ is widely distributed among the agents. They compare these results with observations on wealth distributions of various countries. [2]

In the 2008 article “Pareto and Boltzmann-Gibbs behavior in a Deterministic Multi-agent System, several authors used a Pareto-Boltzmann-Gibbs logic to develop an economic dynamics model in which an economy is a deterministic system of interacting agents. They consider the dynamics of the system to be described by a coupled map lattice with near neighbor interactions, in which the evolution of each agent results from the competition between two factors: the agent's own tendency to grow and the environmental influence that moderates this growth. These authors argue that depending on the values of the parameters that control these factors, the system can display Pareto or Boltzmann-Gibbs statistical behaviors in its asymptotic dynamical regime. [3]

References
1. (a) Vilfredo Pareto - Sociological Theory.
(b) Henderson, Lawrence J. (1935). Pareto's General Sociology: A Physiologists Interpretation. Harvard University Press.
2. Chatterjee , Arnab, Chakrabarti, Bikas K., Manna, S. S. (2003). “Money in Gas-Like Markets: Gibbs and Pareto Laws”, Physica Scripta T106 (2003) 36-38.
3. Gonzalez-Estevez, J., Cosenza, MG, R Lopez-Ruiz, Sanchez, JR. (2008). “Pareto and Boltzmann-Gibbs behaviors in a deterministic multi-agent system” (PDF), Jan 7, Elsevier.
4. (a) Pareto, Vilfredo. (1935). Mind and Society, Volume IV (pg. 1461). New York: Harcourt, Brace.
(b) Bailey, Kenneth D. (1990). Social Entropy Theory (section: “Pareto”, pg. 59-61). State University of New York Press.
5. Stark, Werner. (1962). The Fundamental Forms of Social Thought (quote, 126-27). Routledge.
6. Pareto, Vilfredo. (1896). Course of Political Economics (Cours d’Economie Politique). Publisher.
7. Rigney, Daniel. (2001). The Metaphorical Society: an Invitation to Social Theory (Gibbs, pg. 50). Rowman & Littlefield.

External links
● Vilfredo Pareto – Wikipedia.