5 problems

Locality conjecture. A large class of totally asymmetric models of heat conduction should have a local rate functional for the invariant measure.

Fractional-operator inverse conjecture. The nonequilibrium steady-state energy correlations are given, up to a constant factor $\nu$, by the inverse of the fractional Laplacian:

Let $\kappa(\varepsilon,0)$ denote the conductivity of the deterministic chain at coupling strength $\varepsilon$, and let $n\geq 2$ be any integer. Trivial weak-coupling expansion…

Consider a classical chain of harmonic oscillators with random masses, augmented by an anharmonicity parameter $g$, and let $\kappa(g,\beta)$ denote its heat conductivity at invers…

Consider the infinite anharmonic crystal on $\mathbb Z^d$ with uniform thermostat parameters $\gamma_x=\gamma$ and all thermostats at temperature $T_{\mathrm o}$. Let…