  We define a particular combination of charge and heat currents that is
decoupled with the heat current. This `heat-decoupled' (HD) current can be
transported by diffusion at long distances, when some thermo-electric
conductivities and susceptibilities satisfy a simple condition. Using the
diffusion condition together with the Kelvin formula, we show that the HD
diffusivity can be same as the charge diffusivity and also the heat
diffusivity. We illustrate that such mechanism is implemented in a strongly
coupled field theory, which is dual to a Lifshitz gravity with the dynamical
critical index z=2. In particular, it is exhibited that both charge and heat
diffusivities build the relationship to the quantum chaos. Moreover, we study
the HD diffusivity without imposing the diffusion condition. In some
homogeneous holographic lattices, it is found that the diffusivity/chaos
relation holds independently of any parameters, including the strength of
momentum relaxation, chemical potential, or temperature. We also show a counter
example of the relation and discuss its limited universality.
