In economic thermodynamics, Paul Samuelson (1915-2009) was an American economist noted for his use of analogy concepts from chemistry (e.g. Le Chatelier's principle), physics (equilibrium), thermodynamics (entropy) in various economic theories; for being a second generation student, so to speak, of Willard Gibbs; and for his post-1970s strong vocal skepticism of the use of thermodynamics, particularly entropy, in economic models. Samuelson won the 1970 Nobel Prize in economics for his theories, the second year of the prize. [3]

Education
Samuelson completed his Bachelors from the University of Chicago and his MS (1936) and PhD (1941) from Harvard University. At some point along the line, Samuelson studied under American mathematician Edwin Wilson, who himself had been the sole protégé of American engineer Willard Gibbs, the founder of chemical thermodynamics. In lecture, Wilson had taught Samuelson Le Chatelier’s principle, which explained to Samuelson that in a system (chemical or economic) the changes in the equilibrium is a constrained maximization problem when one of the constraints is marginally tightened or relaxed and thus solved by the “variation principle”. In 1940, he became a professor of economics at MIT.

In the mid 1940s, following a three-year spell in Harvard’s Society of Fellows, an alternative program (founded by Abbott Lawrence and Lawrence Henderson) where students could spend three years pursuing any research that interested them, but were prohibited from working their PhD dissertations, Samuelson quickly wrote his PhD dissertation after which, as the story goes, when he completed his defense of his doctoral dissertation, one member of the committee turned to another and said, “did we pass?” Samuelson’s thesis, according to Andrew W. Lo, modeled each person as an economic agent, and assumed that each individual acted so as to maximize a quantity called ‘expected utility’, a model with which he assumed should be able to predict their behavior in much the same way that physicists predict the behavior of physical objects.

The thesis soon won international acclaim as well as the David A. Wells Prize (1941) for best publishable thesis, and was eventually published in 1947 under the title Foundations of Economic Analysis, the first run 750 copies selling out and soon thereafter was selling at nearly 50,000 copies a year, and would soon become one of the highest selling college textbooks of all time, and as Samuelson latter put it, the work done in his Foundations, won him the 1970 Nobel Prize. [13]

Foundations | 1947
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. [10]

Samuelson | 1960s
In 1960, Samuelson commented: [11]

“The formal mathematical analogy between classical thermodynamics and mathematic economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes – such as entropy or energy – in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should ‘utility’ be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?”

At this point, one can begin to see Samuelson's mind begin to fall apart on this issue. His statement: "why should there be laws like the first or second laws of thermodynamics holding in the economic realm?", is clearly indicative of this. The reversal of this statement is that the first and second laws hold in all systems of the universe, as such the question becomes: "what are the economic determinants involved in the quantification of the governance of the first and second laws in economic terms?"

Samuelson in Washington, DC (1962).

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, Nobel Prize Organization.
3. (a) Mirowski, Philip (1989). More Heat than Light: Economics as Social Physics, Physics as Nature's Economics. Cambridge Univ. Press.
(b) 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.
11. (a) Samuelson, Paul A. (1960). “Structure of a minimum equilibrium system”. In: Pfouts, R.W. (Ed.), Essays in Economics and Econometrics: A Volume in Honor of Harold Hotelling. University of North Carolina Press. Reprinted in Stiglitz, J.E. (Ed.), 1966. The Collected Scientific Papers of Paul A. Samuelson, MIT Press, Cambridge, MA, pp. 651–686.
(b) Smith, Eric and Foley, Duncan. (2008). "Classical Thermodynamics and Economic General Equilibrium Theory", Journal of Economic Dynamics and Control, 32:7-65, Department of Economics Graduate Faculty, New School University, 2005 manuscript.
12. Joyner, James. (2009). “Paul Samuelson, Revolutionary Economist, Dead at 94.” OutsideTheBeltway.com, Dec. 14.
13. Szenberg, Michael, Gottesman, Aron A. and Ramrattan, Lall. (2005). Paul A. Samuelson: on Being an Economist (Samuelson’s 1940 dissertation, pgs. 20-22). Jorge Pinto Books.

Further reading
● Samuelson, Paul A. (1985). “Thermodynamic Theory as Mathematical Economics Could have Discovered It”, Mathematical Social Sciences, 10(3): 281.
● 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.