  We introduce a quantum mechanical formalism for computing the electric
polarization arising in two-dimensional (2D) antiferromagnets (AFMs) as a
result of {\bf both} spin and orbital transport effect of magnons. We first
show that an applied temperature gradient in a 2D collinear honeycomb AFM gives
rise to accumulations of magnons having both orbital moment and spin moment at
the edges of the 2D AFM as the manifestation of the magnon Nernst effects. We
then use our formalism to show that such magnon Nernst effects, in the presence
of the Dzyaloshinskii-Moriya Interaction (DMI), induce electric polarization
that can be measured experimentally. Finally, we demonstrate the value of this
formalism by using it to predict the properties of two 2D honeycomb AFMs, one
each with N\'eel and zigzag order. These results integrate advances in
magnonics, spinorbitronics, and orbitronics to create a unified framework that
can be used to understand and control the manipulation of magnetic states in 2D
AFMs through the magnon spin and orbital degrees of freedom.
