  We study the properties of heat conduction induced by non-Gaussian noises
from athermal environments. We find that new terms should be added to the
conventional Fourier law and the fluctuation theorem for the heat current,
where its average and fluctuation are determined not only by the noise
intensities but also by the non-Gaussian nature of the noises. Our results
explicitly show the absence of the zeroth law of thermodynamics in athermal
systems.
