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We discuss two methods for exploring energy diffusion in lattices with finitetemperature in this paper. The first one is the energy-kick (EK) method. Toapply this method, one adds an external energy kick to a particle in thelattice, and tracks its evolution by evolving the kicked system. The second oneis the fluctuation-correlation (FC) method. The formula for calculating theprobability density function (PDF) using the canonical ensemble is slightlyrevised and extended to the microcanonical ensemble. We show that the FC methodhas advantages over the EK method theoretically and technically. Theoretically,the PDF obtained by the FC method reveals the diffusion processes of the innerenergy while the PDF obtained by the EK method represents that of the kickenergy. The diffusion processes of the inner energy and the external energyadded to the system, i.e., the kick energy, may be different quantitatively andeven qualitatively depending on models. To show these facts, we study not onlythe equilibrium systems but also the stationary nonequilibrium systems.Examples showing that the inner energy and the kick energy may have differentdiffusion behavior are reported in both cases. The technical advantage enablesus to study the long-time diffusion processes and thus avoids the finite-timeeffect.

Methods of exploring energy diffusion in lattices with finite temperature