Diffusion phenomena and thermodynamics

The established theory of linear diffusion phenomena is reformulated in the framework of the non-Hamiltonian dynamical systems theory (Liouville's approach), through the introduction of a suitable characteristic velocity for the processes under consideration. The dissipative features of diffusi...

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Bibliographic Details
Published in:Physics letters. A 2010-07, Vol.374 (34), p.3373-3375
Main Authors: Bertola, V., Cafaro, E.
Format: Article
Language:English
Subjects:
Diffusion
Dissipation
Dynamical systems
Flux
Mathematical analysis
Nonlinearity
Solid state physics
Thermodynamics
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Summary:The established theory of linear diffusion phenomena is reformulated in the framework of the non-Hamiltonian dynamical systems theory (Liouville's approach), through the introduction of a suitable characteristic velocity for the processes under consideration. The dissipative features of diffusion processes are studied in the Riemannian manifold which has flux densities and generalized forces as coordinates, and a tensor metrics defined by the phenomenological coefficients. Some relationships between diffusion phenomena and thermodynamics are explored. Finally, a preliminary extension of the proposed approach to the case of nonlinear constitutive equations is presented, and the effects of non-linearity on the processes dynamics are briefly discussed.
ISSN:0375-9601
1873-2429
DOI:10.1016/j.physleta.2010.06.053