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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1981 Dec;78(12):7839–7843. doi: 10.1073/pnas.78.12.7839

On the entropy function in sociotechnical systems

Elliott W Montroll 1
PMCID: PMC349367  PMID: 16593136

Abstract

The entropy function H = -Σpj log pj (pj being the probability of a system being in state j) and its continuum analogue H = ∫p(x) log p(x) dx are fundamental in Shannon's theory of information transfer in communication systems. It is here shown that the discrete form of H also appears naturally in single-lane traffic flow theory. In merchandising, goods flow from a whole-saler through a retailer to a customer. Certain features of the process may be deduced from price distribution functions derived from Sears Roebuck and Company catalogues. It is found that the dispersion in logarithm of catalogue prices of a given year has remained about constant, independently of the year, for over 75 years. From this it may be inferred that the continuum entropy function for the variable logarithm of price had inadvertently, through Sears Roebuck policies, been maximized for that firm subject to the observed dispersion.

Keywords: Sears Roebuck catalogues, stimulus-response, traffic flow, fluctuations

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Montroll E. W., Shuler K. E. Dynamics of technological evolution: Random walk model for the research enterprise. Proc Natl Acad Sci U S A. 1979 Dec;76(12):6030–6034. doi: 10.1073/pnas.76.12.6030. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Montroll E. W. Social dynamics and the quantifying of social forces. Proc Natl Acad Sci U S A. 1978 Oct;75(10):4633–4637. doi: 10.1073/pnas.75.10.4633. [DOI] [PMC free article] [PubMed] [Google Scholar]

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