Generating Function Formula of Heat Transfer in Harmonic Networks

Details Generating Function Formula of Heat Transfer in Harmonic Networks Generating Function Formula of Heat Transfer in Harmonic Networks

2010-12-03

arxiv.org/abs/1012.0622v2

Phys. Rev. E vol.83 041121 (2011)

Physics

Condensed Matter

Statistical Mechanics

5 pages, 1 figure

Scientific paper

We consider heat transfer across an arbitrary harmonic network connected to two heat baths at different temperatures. The network has $N$ positional degrees of freedom, of which $N_L$ are connected to a bath at temperature $T_L$ and $N_R$ are connected to a bath at temperature $T_R$. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for $N_L \ne N_R$ and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.

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