Massimo Materassi and Emanuele Tassi. Algebrizing friction: a brief look at the Metriplectic Formalism

Natural Sciences / Astronomy / General physics

Submitted on: Jul 28, 2012, 03:34:23

Description: The formulation of Action Principles in Physics, and the introduction of the Hamiltonian framework, reduced dynamics to bracket algebrae of observables. Such a framework has great potentialities, to understand the role of symmetries, or to give rise to the quantization rule of modern microscopic Physics. Conservative systems are easily algebrized via the Hamiltonian dynamics: a conserved observable H generates the variation of any quantity f via the Poisson bracket {f,H}. Recently, dissipative dynamical systems have been algebrized in the scheme presented here, referred to as metriplectic framework: the dynamics of an isolated system with dissipation is regarded as the sum of a Hamiltonian component, generated by H via a Poisson bracket algebra; plus dissipation terms, produced by a certain quantity S via a new symmetric bracket. This S is in involution with any other observable and is interpreted as the entropy of those degrees of freedom statistically encoded in friction. In the present paper, the metriplectic framework is shown for two original "textbook" examples. Then, dissipative Magneto-Hydrodynamics (MHD), a theory of major use in many space physics and nuclear fusion applications, is reformulated in metriplectic terms.

The abstract of this article has been published in the "Intellectual Archive Bulletin" , July 2012, ISSN 1929-1329.

The full-text article has been published in the "IntellectualArchive" journal , Vol.1, Num.3, July 2012, ISSN 1929-4700.

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Materassi Tassi Chaos 2011.pdf

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