Validity of local thermal equilibrium in anomalous heat diffusion

Local thermal equilibrium (LTE) is a general presumption of many theoretical analyses in nonequilibrium statistical physics. It describes a situation that although the system is not in global thermal equilibrium, each small portion of the system may still be described approximately by the laws of thermal equilibrium. The validity of LTE has however seldom been investigated carefully. Here, by studying the ensemble velocity distribution and its spatial correlation, we present strong evidences for the lack of LTE in anomalous heat diffusion processes in one dimensional harmonic lattices and the Fermi-Pasta-Ulam-beta lattices. In particular, clear nonzero excess kurtosis and long range correlations have been observed, with values scaling linearly with the initial temperature difference. Therefore near thermal equilibrium is not sufficient to achieve LTE. Some existing studies that are based on the existence of LTE should be revisited. Using the same methods, we also show that LTE is still valid in the phi(4) lattice, in which heat diffuses following Fourier's law.