Generating Function Formula of Heat Transfer in Harmonic Networks

Abstract

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.

5 pages, 1 figure

References in corpus (9)

• Heat Transport in low-dimensional systems
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Symmetry in Full Counting Statistics, Fluctuation Theorem, and Relations among Nonlinear Transport Coefficients in the Presence of a Magnetic Field
• Heat transport in harmonic lattices
• Work fluctuation theorems for harmonic oscillators
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Fluctuation theorem and large deviation function for a solvable model of a molecular motor
• Large deviations of heat flow in harmonic chains
• Heat conduction and phonon localization in disordered harmonic crystals

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