4 problems

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Anharmonicity conjecture for Fourier's law in oscillator chains
Consider a one-dimensional oscillator chain with microscopic energy current and finite-size conductivity … Fourier's law asks for a finite, nonzero thermodynamic conductivity…
Conjectureopenkinetic-theory oscillator-chains transport-theoryarXiv posted 2 days ago
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Collisional-invariant conjecture for generic oscillator-chain dispersion relations
Let $\omega$ be a dispersion relation on $\mathbb{T}$ , and let $g$ satisfy the collisional-invariant equation … For the unpinned nearest-neighbor dispersion relation…
Conjectureopencollisional-invariants kinetic-theory oscillator-chainsarXiv posted 2 days ago
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Conjecture on convergence for a chain with the center at site n
Let $k$ be the exponent in the pinning potential, and let $n$ denote the center of the chain. Convergence conjecture. The asserted convergence is true as soon as … This conjecture…
Conjectureopennonequilibrium-statistical-mechanics oscillator-chainsarXiv posted 2 days ago
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Conjecture on superpolynomial decay of thermal conductivity at high temperature
High-temperature conductivity conjecture. For both chains,
Conjectureopenhigh-temperature-asymptotics oscillator-chains thermal-conductivityarXiv posted 2 days ago

Anharmonicity conjecture for Fourier's law in oscillator chains