| Journal: | Revista mexicana de física E |
| Database: | PERIÓDICA |
| System number: | 000343006 |
| ISSN: | 1870-3542 |
| Authors: | Schonfeldt, J.H1 Rostona, G.B1 Plastino, A.R1 Plastino, A2 |
| Institutions: | 1University of Pretoria, Department of Physics, Pretoria, Transvaal. Sudáfrica 2Universidad Nacional de La Plata, Facultad de Ciencias Exactas, La Plata, Buenos Aires. Argentina |
| Year: | 2006 |
| Season: | Dic |
| Volumen: | 52 |
| Number: | 2 |
| Pages: | 151-159 |
| Country: | México |
| Language: | Español |
| Document type: | Artículo |
| Approach: | Experimental, aplicado |
| Spanish abstract | El panorama de la f´ısica contempor´anea se encuentra en un estado de continuo cambio y por ende la estructura de los planes de estudio del ´area necesita adaptarse a tal situaci´on. La creciente importancia de la multidisciplinariedad es hoy faceta t´ıpica de la actividad en f´ısica. T´ecnicas e ideas de origen f´ısico est´an siendo aplicados con ´exito en ´areas diversas. Biolog´ıa y econom´ıa constituyen ejemplos importantes. La f´ısica estad´ıstica (FE) es la principal proveedora de m´etodos para este tipo de aplicaciones. Este trabajo se refiere a una idea muy fecunda (y de amplia aplicaci´on) de la FE, el llamado “principio de m´axima entrop´ıa” (PME). Pretendemos aqu´ı mostrar como puede el PME ser integrado con provecho en la curr´ıcula de la f´ısica. Se ver´a que los cursos de mec´anica estad´ıstica no son los ´unicos donde este principio puede ser exitosamente incorporado. En particular, ilustraremos como el PME puede ser empleado para construir soluciones anal´ıticas relativamente sencillas para ecuaciones de evoluci´on muy importantes, tales como las de Liouville y Fokker-Planck |
| English abstract | 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 |
| Disciplines: | Física y astronomía, Matemáticas, Educación |
| Keyword: | Termodinámica y física estadística, Didáctica, Educación superior, Principio de máxima entropía, Ecuación de continuidad, Ecuación de Liouville |
| Keyword: | Physics and astronomy, Mathematics, Education, Thermodynamics and statistical physics, Didactics, Higher education, Maximum entropy principle, Continuity equations, Liouville equation |
| Full text: | Texto completo (Ver PDF) |
