[en] We study the heat current autocorrelation function (HCAF) in one-dimensional, momentum-conserving lattices. In particular, we explore if there is any link between the decaying characteristics of the HCAF and asymmetric interparticle interactions. The Lennard-Jones model is investigated intensively in view of its significance to applications. It is found that, in the time range accessible to numerical simulations, the HCAF decays faster than power-law manners, and in some cases it decays even exponentially. Following the Green–Kubo formula, fast decay of the HCAF implies convergence of the heat conductivity, which is also corroborated by simulations. In addition, with a comparison to the Fermi–Pasta–Ulam-β model of symmetric interactions, the HCAF of the Fermi–Pasta–Ulam-α–β model of asymmetric interactions is also investigated. The results of all these studies lead to that, in certain ranges of parameters, fast decaying of the HCAF can be observed and correlated to the asymmetry degree of interactions. (paper: classical statistical mechanics, equilibrium and non-equilibrium)