3 problems

Consider a one-dimensional oscillator chain with microscopic energy current and finite-size conductivity … Fourier's law asks for a finite, nonzero thermodynamic conductivity…

Grosjean's modified diffusion-length conjecture. The modified diffusion length can be obtained without Fourier transforms using only $\langle s^2\rangle$, and the complete Grosjean…

General-dimensional diffusion-coefficient conjecture. The formula $D=\langle s^2\rangle/(2d)$ holds in arbitrary spatial dimension $d$, with the dependence on $d$ as indicated.