  We study heat current and the full statistics of heat fluctuations in a
capacitively-coupled double quantum dot system. This work is motivated by
recent theoretical studies and experimental works on heat currents in quantum
dot circuits. As expected intuitively, within the (static) mean-field
approximation, the system at steady-state decouples into two single-dot
equilibrium systems with renormalized dot energies, leading to zero average
heat flux and fluctuations. This reveals that dynamic correlations induced
between electrons on the dots is solely responsible for the heat transport
between the two reservoirs. To study heat current fluctuations, we compute
steady-state cumulant generating function for heat exchanged between reservoirs
using two approaches : Lindblad quantum master equation approach, which is
valid for arbitrary coulomb interaction strength but weak system-reservoir
coupling strength, and the saddle point approximation for Schwinger-Keldysh
coherent state path integral, which is valid for arbitrary system-reservoir
coupling strength but weak coulomb interaction strength. Using thus obtained
generating functions, we verify steady-state fluctuation theorem for stochastic
heat flux and study the average heat current and its fluctuations. We find that
the heat current and its fluctuations change non-monotonically with the coulomb
interaction strength ($U$) and system-reservoir coupling strength ($\Gamma$)
and are suppressed for large values of $U$ and $\Gamma$.
