In economic thermodynamics, Paul Anthony Samuelson (1915-) is an American economist noted for his use of concepts from chemistry (e.g. Le Chatelier's principle), physics (equilibrium), thermodynamics (entropy) in various economic theories. Of Nobel Prize winners in thermodynamics, Samuelson won the 1970 Nobel Prize in Economics, the second year of the prize. [3]

Gibbs and Wilson
Samuelson's general economic model, in particular, was influenced by Gibbsian equilibrium criterion. His 1947 book Foundations of Economic Analysis, from his doctoral dissertation, is based, in theme, on Gibbs' 1876 On the Equilibrium of Heterogeneous Substances. [1] Samuelson was the sole protegé of the polymath Edwin Wilson, who had himself been the sole protegé of Yale's great physicist Willard Gibbs. [2] During these formative years, Gibbs' theories on equilibrium and chemical thermodynamics influenced them both in their ideas on the equilibrium of economic systems.

In his seminal Foundations, Samuelson suggested, for example, that variation of the demand for a factor with a change in its price was analytically similar to thermodynamic variation in the pressure, volume, and temperature of an ideal gas. [9] All of this is pure Gibbsian. In fact, one may argue that the terms "foundation" and "variation" were plucked directly from the first page of the abstract to Equilibrium, wherein Gibbs states:

"Little has been done to develop the principle [of entropy] as a foundation for the general theory of thermodynamic equilibrium, which may be reformulated as follows: for the equilibrium of any isolated system it is necessary and sufficient that in all possible variations of the state of the system which do not alter its energy, the variation [δ] of its entropy shall either vanish or be negative."

In short, Samuelson seemed to have adopted the variational logic of differential equations employed in thermodynamics, where variation goes by the mathematical name of "derivative", to be applied in economics. Samuelson, however, maintains that his borrowing of thermodynamics to application in theoretical economics is only as “mathematical isomorphisms” between the maximum-minimum structures of thermodynamics and the cost-profit-utility systems of economics.

Samuelson in Washington, DC (1962).

[10]
Entropy pessimism
Curiously, although Samuelson used and discussed thermodynamics in his own work, he seemed to become more and more pessimistic of the use of entropy and thermodynamics in general by others, especially in his later years, particularly after his 1970 Nobel prize win. In 1972, for instance, in a dismissal of the idea of a sociological thermodynamics, Samuelson concluded: [4]

"The sign of a half-baked speculator in the social sciences is his search for something in the social system that corresponds to the physicist's notion of entropy."

Yet, in 1974, Samuelson wrote that a high-PQ trader “is in effect possessed of a ‘Maxwell’s demon’ who tells him how to make capital gains from effective peek into tomorrow’s financial page reports.” [7] Again, in the 1980 edition of his famous Economics textbook, he outlines a discussion on “entropy economics”. In the same work, he outlines how, in his view, energy and entropy are consequential for economics: [6]

“You can’t make a perpetual motion machine that will run by dropping a ball’s bouncing back to higher than its point of release. That’s a consequence of the first law of thermodynamics—which guarantees conservation (or constancy of the total energy). More subtle, but no less consequential for economics, is the second law of thermodynamics: it requires that the total entropy (or ‘disorder’) irreversibly increases, while the total of energy is remained constant.”

So, on one hand (1972), he states that people who use entropy in the social sciences are half-baked, yet he advises its use in economics on the other hand (1980); a point of inconsistency in his mind? A turning point in the mind of Samuelson occurred following the publication of the eleventh edition (1980) of his Economics. In subsequent editions (after the eleventh), noted Egyptian-born American physicist Jack Hokikian, all mentions of entropy and the laws of thermodynamics had been removed? [8]

At the 1989 Gibbs Symposium, organized to honor the memory of the theoretical physicist Willard Gibbs on the 150th anniversary of his birth, Samuelson had become even more pessimistic on the use of thermodynamics in economics:

“As will become apparent, I have limited tolerance for the perpetual attempts to fabricate for economics concepts of ‘entropy’ imported from the physical sciences or constructed by analogy to Clausius-Boltzmann magnitudes”.

He continues: [5]

“The monthly mail still brings grandiose schemes to replace the dollar as a unit of value by energy or entropy units. Superficial knowledge of thermodynamics, brought into contact with ignorance of economics, cannot even in the presence of the catalyst of noble intentions beget stable equilibrium of useful of useful products. This is not a tautology, merely a finding of fifty-five years of reading the morning mail.”

Whatever the reason, it is very curious that a student of Gibbs would find such irritation at the use of energy and entropy in the study of economic systems?

References
1. (a) Caldi, D. G. and Mostow, George D. (1989). Proceedings of the Gibbs Symposium, May 15-17, (section: Gibbs in economics, by Paul Samuelson, pgs. 255-68). American Mathematical Society.
(b) Samuelson, P. A. (1983). Foundations of Economic Analysis (extended edition). Holiday House.
(c) Jolls, K. R. (1990). Gibbs and the art of thermodynamics, Gibbs in economics, Proceedings of the Gibbs Symposium (Providence, R.I.), 293-321.
2. Samuelson, Paul (2003). "How I Became an Economist", 1970 Laureate in Economics, 5 September, Noble Prize Organization.
3. (a) Smith, Eric & Foley, Duncan. (2005). "Classical Thermodynamics and Economic General Equilibrium Theory." [PDF], Department of Economics Graduate Faculty, New School University.
(b) Mirowski, Philip (1989). More Heat than Light: Economics as Social Physics, Physics as Nature's Economics. Cambridge Univ. Press.
(c) Samuelson, P. A. (1970). "Maximum Principles in Analytical Economics", Nobel Prize Lecture.
4. Samuelson, Paul. (1972). The Collected Scientific Papers (pg. 450). Vol. 3, ed. R. Merton. Cambridge, Mass.: MIT Press.
5. Caldi, D. G. and Mostow, George D. (1989). Proceedings of the Gibbs Symposium, May 15-17, (section: Gibbs in economics, by Paul Samuelson, pgs. 255-68). American Mathematical Society.
6. Samuelson, Paul A. (1980). Economics, 11th ed. (pg. 747). McGraw-Hill.
7. Poundstone, William. (2006). Fortune’s Formula (pgs. 207, 346). MacMillan.
8. Hokikian, Jack. (2002). The Science of Disorder: Understanding the Complexity, Uncertainty, and Pollution in Our World (pg. 235). Los Feliz Publishing.
9. Mirowski, Philip. (1988). Against Mechanism: How to Protect Economics from Science (pg. 94). Rowman & Littlefield.
10. Liossatos, Panagis, S. (2004). "Statistical Entropy in General Equilibrium Theory." Department of Economics, Florida International University.

Further reading
● Samuelson, Paul A. (1990). “Gibbs in Economics (subsection: How thermodynamics impacts economics, pg. 263-)” (pgs. 255-68); in Proceedings of the Gibbs Symposium: Yale University, May 15-17, 1989 by D.G. Caldi, George D. Mostow, American Mathematical Society, 1990.

External links
● Paul Samuelson – Wikipedia.