  Recent experiments at the nanoscales confirm that thermal rectifiers, the
thermal equivalent of electrical diodes, can operate in the quantum regime. We
present a thorough investigation of the effect of different particle exchange
statistics, coherence, and collective interactions on the quantum heat
transport of rectifiers with two-terminal junctions. Using a collision model
approach to describe the open system dynamics, we obtain a general expression
of the nonlinear heat flow that fundamentally deviates from the Landauer
formula whenever quantum statistical or coherence asymmetries are present in
the bath particles. Building on this, we show that heat rectification is
possible even with symmetric medium-bath couplings if the two baths differ in
quantum statistics or coherence. Furthermore, the associated thermal
conductance vanishes exponentially at low temperatures as in the
Coulomb-blockade effect. However, at high temperatures it acquires a power-law
behavior depending on the quantum statistics. Our results can be significant
for heat management in hybrid open quantum systems or solid-state thermal
circuits.
