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Título del libro: Variational And Extremum Principles In Macroscopic Systems
Título del capítulo: Variational principles for irreversible hyperbolic transport

Autores UNAM:
JESUS ANTONIO DEL RIO PORTILLA; MARIANO LOPEZ DE HARO;
Autores externos:

Idioma:
Inglés
Año de publicación:
2005
Resumen:

This chapter explains the variational formulations of irreversible hyperbolic transport. It illustrates the restricted variational principles as they are applied to extended irreversible thermodynamics for the cases of the soil-water system and heat transport in solids. This kind of restricted variational principles leads to the time-evolution equations for the non-conserved variables as extreme conditions. In particular, as has been noted in the case of heat transport, this perspective may provide interesting generalizations of the well-known Maxwell-Cattaneo-Vernotte forms. In order to show how a Poissonian structure may be obtained, a formulation in terms of the so-called variational potentials is described and used to derive the time evolution of the fluctuations in hyperbolic transport. These fluctuations are shown to obey the Chapman-Kolmogorov equation. The case of relativistic heat transport is discussed as an example of such formulation. The hyperbolic transport is also analyzed in the framework of the path-integral approach. This latter methodology allows for the consideration of nonlinear hyperbolic transport, in contrast with what occurs in the case of the variational potentials scheme. © 2005 Elsevier B.V. All rights reserved.


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