7 problems

Finite-system conductivity conjecture. $\kappa_N$ and, respectively, $\tilde\kappa_N$, should have the same asymptotic behavior as the conductivity defined in that nonequilibrium s…

Consider the one-dimensional charged harmonic oscillator model with staggered magnetic field, denoted by case $(ii)$, and let $\kappa^{(ii)}_{\beta}(t)$ be its infinite-volume cano…

The model consists of charged harmonic oscillators arranged on a $d$-dimensional lattice, with each oscillator moving in a $d^*$-dimensional space, where $d^*\geq 2$ so that a magn…

Gaspard–Gilbert universality conjecture. The displayed equalities should hold for more general stochastic energy-exchange models obtained from locally confined collision dynamics.…

High-temperature conductivity conjecture. For both chains,

Conductivity bound conjecture. In this later case, one should have

Finite-volume Green–Kubo convergence conjecture. For fixed positive $\lambda$, as $N$ tends to infinity, the finite-volume dynamics converges to the infinite-volume dynamics in the…