Resumo
This Nota de Física aims to shed further light on the origin of the cuspidal temperature profile of non-equilibrium chains, namely the 1967 Rieder, Liebowitz and Lieb heat conduction model.Our upgraded analysis shows that the first plateau -- where the cumulants of the heat flux reach their maxima -- is related to the vanishing of the (instantaneous) stationary state two-point velocity correlations for all pairs of elements in the chain, $C_{v}(i,j) \equiv \lim _{t \rightarrow \infty} \left\langle v_i \left(t\right) v_j \left(t\right) \right\rangle =0 $. Such behaviour is equivalent to having a ``phonon box''. For the second plateau, $C_{v}(i,j)$ only vanishes when one of the sites is a edge site; however, the sum of the stationary state two-point velocity correlations over all pairs still equals zero, $\sum _{\left\langle ij\right\rangle} C_{v}(i,j) =0$, as happens whenever the chain is linear.
Bringing the non-linear $\beta$-Fermi-Pasta-Ulam nonequilibrium model into play, we verify that the bulk plateau disappears and that in this situation $\sum _{\left\langle ij\right\rangle} C_{v}(i,j) \neq 0$.
These results confirm a relation between heat transport in non-equilibrium systems and a spatial propagator that is proxied by $C_{v}(i,j)$.