Maximum entropy principle, evolution equations, and physics education

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Main Author:	J-H. Schonfeldt
Format:	Artículo científico
Language:	en
Published:	Sociedad Mexicana de Física A.C. 2006
Subjects:	Física, Astronomía y Matemáticas Liouville equation continuity equations Maximum entropy principle
Online Access:	Acceder al recurso
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author	J-H. Schonfeldt
author_facet	J-H. Schonfeldt
contents	Maximum entropy principle, evolution equations, and physics education J-H. Schonfeldt G. B. Roston A. R. Plastino A. Plastino Física, Astronomía y Matemáticas Liouville equation continuity equations Maximum entropy principle The landscape of Physics is in a constant state of change and the structure of the University level Physics Curriculum needs to be adapted to this state of affairs. One of the most interesting current features of physics is the increasing importance of multidisciplinary studies. Methods and ideas from physics are being applied to diverse areas of science ranging from biology and economics to sociology and linguistics. Statistical Physics (SP) provides the most fertile set of methods for these kind of applications. The aim of the present contribution is to show how a powerful idea from SP that is widely applied in many fields, the maximum entropy principle (MaxEnt), can be integrated into the physics curriculum. First of all, the constrained maximization of an entropic measure provides an important illustration of the Lagrange multipliers technique, which is part of the standard calculus course for physics students. Secondly, MaxEnt provides the basis for an alternative foundation for statistical mechanics, which is nowadays being considered in some modern textbooks on SP. In point of fact, the main role usually assigned to MaxEnt (as a tool for teaching theoretical physics) is in connection with the Gibbs canonical and grand canonical ensembles. However, as we shall here explain, MaxEnt also constitutes a useful tool in the teaching of other aspects of theoretical physics: it provides an elegant and simple method for obtaining analytical solutions for several evolution equations, like the Liouville equation, the diffusion equation, and the Fokker-Planck equation. Last but certainly not least, MaxEnt belongs to the tool-kit that physicist use to solve concrete "real-world" problems. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065607 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.52
format	Artículo científico
id	redalyc_57065607
language	en
publishDate	2006
publisher	Sociedad Mexicana de Física A.C.
spellingShingle	Maximum entropy principle, evolution equations, and physics education J-H. Schonfeldt Física, Astronomía y Matemáticas Liouville equation continuity equations Maximum entropy principle Maximum entropy principle, evolution equations, and physics education J-H. Schonfeldt G. B. Roston A. R. Plastino A. Plastino Física, Astronomía y Matemáticas Liouville equation continuity equations Maximum entropy principle The landscape of Physics is in a constant state of change and the structure of the University level Physics Curriculum needs to be adapted to this state of affairs. One of the most interesting current features of physics is the increasing importance of multidisciplinary studies. Methods and ideas from physics are being applied to diverse areas of science ranging from biology and economics to sociology and linguistics. Statistical Physics (SP) provides the most fertile set of methods for these kind of applications. The aim of the present contribution is to show how a powerful idea from SP that is widely applied in many fields, the maximum entropy principle (MaxEnt), can be integrated into the physics curriculum. First of all, the constrained maximization of an entropic measure provides an important illustration of the Lagrange multipliers technique, which is part of the standard calculus course for physics students. Secondly, MaxEnt provides the basis for an alternative foundation for statistical mechanics, which is nowadays being considered in some modern textbooks on SP. In point of fact, the main role usually assigned to MaxEnt (as a tool for teaching theoretical physics) is in connection with the Gibbs canonical and grand canonical ensembles. However, as we shall here explain, MaxEnt also constitutes a useful tool in the teaching of other aspects of theoretical physics: it provides an elegant and simple method for obtaining analytical solutions for several evolution equations, like the Liouville equation, the diffusion equation, and the Fokker-Planck equation. Last but certainly not least, MaxEnt belongs to the tool-kit that physicist use to solve concrete "real-world" problems. 2006 artículo científico 0035-001X https://www.redalyc.org/articulo.oa?id=57065607 en http://www.redalyc.org/revista.oa?id=570 Revista Mexicana de Física application/pdf Sociedad Mexicana de Física A.C. Revista Mexicana de Física (México) Num.2 Vol.52
title	Maximum entropy principle, evolution equations, and physics education
topic	Física, Astronomía y Matemáticas Liouville equation continuity equations Maximum entropy principle
url	https://www.redalyc.org/articulo.oa?id=57065607

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