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Generating function formula of heat transfer in harmonic networks
1Graduate School of Science, University of Tokyo, 113-0033, Japan.
Summary
Researchers derived an exact formula for heat transfer in classical harmonic networks. This formula, valid across different transport regimes, confirms the Gallavotti-Cohen fluctuation symmetry for nonequilibrium systems.
Area of Science:
- Statistical Mechanics
- Condensed Matter Physics
- Non-equilibrium Thermodynamics
Background:
- Heat transfer in classical harmonic networks is crucial for understanding thermal transport.
- Different transport regimes (ballistic, anomalous, diffusive) exist in harmonic crystals.
- The Gallavotti-Cohen fluctuation symmetry is a key principle in non-equilibrium statistical mechanics.
Purpose of the Study:
- To derive an exact formula for the cumulant generating function of heat transfer.
- To investigate the validity of the Gallavotti-Cohen fluctuation symmetry in harmonic networks.
- To provide a tool for studying non-equilibrium current fluctuations.
Main Methods:
- Analysis of heat transfer across a classical harmonic network with N degrees of freedom.
- Connection to two heat baths at different temperatures (T(L) and T(R)).
- Derivation of an exact formula for the cumulant generating function.
Main Results:
- An exact formula for the cumulant generating function of heat transfer was derived.
- The formula is valid for unequal numbers of connected sites (N(L)≠N(R)).
- The derived formula satisfies the Gallavotti-Cohen fluctuation symmetry.
Conclusions:
- The derived formula confirms the Gallavotti-Cohen fluctuation symmetry in all transport regimes of harmonic crystals.
- This exact formula serves as a powerful tool for analyzing non-equilibrium current fluctuations.
- The findings have implications for understanding thermal transport in complex systems.
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