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Title: The interactional foundations of MaxEnt: Open questions

Abstract

One of the simplest and potentially most useful techniques to be developed in the 20{sup th} century, a century noted for an ever more mathematically sophisticated formulation of the sciences, is that of maximising the entropy of a system in order to generate a descriptive, stochastic model of that system in closed form, often abbreviated to MaxEnt. The extension of MaxEnt to systems beyond the physics from which it originated is hampered by the fact that the microscopic physical interactions that are not justified or justifiable within the MaxEnt framework need to be falsifiably evaluated in each new field of application. It is not obvious that such justification exists for many systems in which the interactions are not directly based on physics. For example what is the justification for the use of MaxEnt in biology, climate modelling or economics? Is it simply a useful heuristic or is there some deeper connection with the foundations of some systems? Without further critical examination of the microscopic foundations that give rise to the success of the MaxEnt principle it is difficult to motivate the use of such techniques in other fields except through theoretically an practically unsatisfying analogical arguments. This article briefly presentsmore » the basis of MaxEnt principles as originally introduced in statistical mechanics in the Jaynes form, the Tsallis form and the Rényi form. Several different applications are introduced including that of ecological diversity where maximising the different diversity measures is equivalent to maximising different entropic functionals.« less

Authors:
 [1]
  1. Complex Systems Research Group, School of Civil Engineering, The University of Sydney, Sydney NSW 2006 (Australia)
Publication Date:
OSTI Identifier:
22390758
Resource Type:
Journal Article
Journal Name:
AIP Conference Proceedings
Additional Journal Information:
Journal Volume: 1636; Journal Issue: 1; Conference: MaxEnt 2013: 33. International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, Canberra, ACT (Australia), 15-20 Dec 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094-243X
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ENTROPY; EV RANGE; FUNCTIONALS; M CODES; MATHEMATICAL MODELS; STATISTICAL MECHANICS; STOCHASTIC PROCESSES

Citation Formats

Harré, Michael S., E-mail: michael.harre@sydney.edu.au. The interactional foundations of MaxEnt: Open questions. United States: N. p., 2014. Web. doi:10.1063/1.4903704.
Harré, Michael S., E-mail: michael.harre@sydney.edu.au. The interactional foundations of MaxEnt: Open questions. United States. https://doi.org/10.1063/1.4903704
Harré, Michael S., E-mail: michael.harre@sydney.edu.au. 2014. "The interactional foundations of MaxEnt: Open questions". United States. https://doi.org/10.1063/1.4903704.
@article{osti_22390758,
title = {The interactional foundations of MaxEnt: Open questions},
author = {Harré, Michael S., E-mail: michael.harre@sydney.edu.au},
abstractNote = {One of the simplest and potentially most useful techniques to be developed in the 20{sup th} century, a century noted for an ever more mathematically sophisticated formulation of the sciences, is that of maximising the entropy of a system in order to generate a descriptive, stochastic model of that system in closed form, often abbreviated to MaxEnt. The extension of MaxEnt to systems beyond the physics from which it originated is hampered by the fact that the microscopic physical interactions that are not justified or justifiable within the MaxEnt framework need to be falsifiably evaluated in each new field of application. It is not obvious that such justification exists for many systems in which the interactions are not directly based on physics. For example what is the justification for the use of MaxEnt in biology, climate modelling or economics? Is it simply a useful heuristic or is there some deeper connection with the foundations of some systems? Without further critical examination of the microscopic foundations that give rise to the success of the MaxEnt principle it is difficult to motivate the use of such techniques in other fields except through theoretically an practically unsatisfying analogical arguments. This article briefly presents the basis of MaxEnt principles as originally introduced in statistical mechanics in the Jaynes form, the Tsallis form and the Rényi form. Several different applications are introduced including that of ecological diversity where maximising the different diversity measures is equivalent to maximising different entropic functionals.},
doi = {10.1063/1.4903704},
url = {https://www.osti.gov/biblio/22390758}, journal = {AIP Conference Proceedings},
issn = {0094-243X},
number = 1,
volume = 1636,
place = {United States},
year = {Fri Dec 05 00:00:00 EST 2014},
month = {Fri Dec 05 00:00:00 EST 2014}
}