# Elliott Montroll

In human physics, Elliott Montroll (1916-1983) was an American chemist, mathematician, physicist, and statistical mechanicist noted for his 1974 Introduction to Quantitative Aspects of Social Phenomena, coauthored with Wade Badger, which tends to get cited in econophysics histories as being on the first books to apply statistical physics methods to sociology, or something along these lines. [1] Montroll and Badger, in their book, discuss the application of probability to traffic flow, income distributions, floods, and the stock market. [3]

Molecular comparisons
Montroll seems to employ a certain number of humans to molecules comparisons (see: human molecular formula), and in one section of this book give the following formula for the total kinetic energy of the$i^{th} \,$molecule in a system, being supposedly a socioeconomic system:

$\epsilon_i(x) = \frac{1}{2} m u_i^2 \,$

where m is mass and ui the velocity of the molecule, respectively, then comments:

“The [acts of a human] individual [occurs] in a manner to that in which energy is transferred from gas molecule to gas molecule by collisions. Through transfer of goods or services (or welfare), every family has someone with an annual income. One might argue that through many transactions money tends to get randomly distributed but, through some unclear constraints which are due to training, motivation, risk-taking, inheritance, intimidation etc., some people obtain [more money].”

This is pretty decent logic. Here, Montroll seems to be making a reference to the Pareto principle of wealth distribution.

Other
Montroll has also commented on the Vienna school of statistical thermodynamics. [2]

References
1. (a) Montroll, Elliott and Badger, Wade W. (1974). Introduction to Quantitative Aspects of Social Phenomena (molecule, 5+ pgs; quote, pg. 158; entropy, 11+ pgs). Gordon and Breach.
(b) Yakovenko, Victor M. (2009). “Econophysics, Statistical Mechanics, An Approach to”, in: Encyclopedia of Complexity and System Science (editors: R.A. Meyers) (abs). Springer.
(c) Savoiu, Gheorghe. (2012). Econophysics: Background and Applications in Economics, Finance, and Sociophysics (pg. 8). Academic Press.
2. Montroll, Elliott W. (1984). “On the Vienna School of Statistical Thought.”, AIP Conf. Proc. Feb. 28, Vol. 109, (pgs 1-10).
3. Gould, Harvey Tobochnik, Jan. (2010). Statistical and Thermal Physics: with Computer Applications (pg. 178). Princeton University Press.

Further reading
● Montroll, Elliott W. (1977). “On Some Mathematical Models of Social Phenomena” in: Nonlinear Equations in Abstract Spaces (pgs. 161-216), Proc. International Symposium, University of Texas, Arlington. Academic Press.
● Montroll, Elliott W. (1978). “Social Dynamics and the Quantifying of Social Forces” (abs) (pdf), Proceedings of the National Academy of Science, USA, 75(10):4633-37.
● Montroll, Elliott W. (1981). “On the Dynamics of the Ising Model of Cooperative Phenomena”, Proceedings of the National Academy of Science,USA, 78(1):36-40.
● Montroll, Elliott W. (1981). “On the Entropy Function in Sociotechnical Systems”, Proclamations of the National Academy of Science USA, 78(12);7839-43.
● Montroll, Elliott W. (1987). “On the Dynamics and Evolution of Some Sociotechnical Systems” (abs) (pdf), Bulletin of the American Mathematical Society, 16:1-46.

External links
Elliott Montroll – Wikipedia.