Multiscale thermodynamics and mechanics of heat

Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distributio...

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Published in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-06, Vol.83 (6 Pt 1), p.061134-061134, Article 061134
Main Authors: Grmela, Miroslav, Lebon, Georgy, Dubois, Charles
Format: Article
Language:English
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Summary:Heat transfer is investigated on three levels of description: Fourier, Cattaneo, and Peierls. The microscopic nature of the heat that becomes important, in particular in nanoscale systems, is characterized by a vector field related to the heat flux on the Cattaneo level and by the phonon distribution function on the Peierls level. All dynamical theories discussed in the paper are fully nonlinear and all are proven to be compatible among themselves, with equilibrium thermodynamics, and with mechanics. An investigation of the first two compatibilities gives rise to potentials having the physical interpretation of nonequilibrium entropies. The compatibility with mechanics is manifested by the Hamiltonian structure of the time-reversible part of the time evolution.
ISSN:1539-3755
1550-2376
DOI:10.1103/physreve.83.061134