We investigate heat conduction in the multiscale setting involving
the Fourier, the Cattaneo, and the Peierls theories. Thermodynamics
emerges in the passages among the scales. The time
evolution appearing in the more microscopic theory (i.e. the theory
involving more microscopic details) is split into the fast (reducing)
and the slow (reduced) time evolution. During the reducing
time evolution the extra state variables chosen to characterize
the details become completely subjugated to the state variables
used in the reduced time evolution. The reducing time evolution
is generated by a potential that, if evaluated at the state reached
asymptotically in the reducing time evolution, becomes a novel
thermodynamic potential on the reduced level.
Papers presented at the 13th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Portoroz, Slovenia on 17-19 July 2017 .
Murphy, Raegan(University of Pretoria, 2007-11-12)
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