  We study diffusion processes of local fluctuations of heat, energy, momentum,
and mass in three paradigmatic one-dimensional systems. For each system,
diffusion processes of four physical quantities are simulated and the cross
correlations between them are investigated. We find that, in all three systems,
diffusion processes of energy and mass can be perfectly expressed as a linear
combination of those of heat and momentum, suggesting that diffusion processes
of heat and momentum may represent the heat mode and the sound mode in the
hydrodynamic theory. In addition, the dynamic structure factor, which describes
the diffusion behavior of local mass density fluctuations, is in general
insufficient for probing diffusion processes of other quantities because in
some cases there is no correlation between them. We also find that the
diffusion behavior of heat can be qualitatively different from that of energy,
and, as a result, previous studies trying to relate heat conduction to energy
diffusion should be revisited.
