  Understanding the statistics of quasi-particle excitations in magnetic
systems is essential for exploring new magnetic phases and collective quantum
phenomena. While the chemical potential of a ferromagnetic gas has been
extensively investigated both theoretically and experimentally, its
antiferromagnetic counterpart remains uncharted. Here, we derive the statistics
of a two-component U(1)-symmetric Bose gas and apply our results to an
axially-symmetric antiferromagnetic insulator. We find that the two magnon
eigenmodes of the system are described by an equal and opposite chemical
potential, in analogy with a particle-antiparticle pair. Furthermore, we derive
the thermomagnonic torques describing the interaction between the coherent and
incoherent antiferromagnetic spin dynamics. Our results show that the magnitude
and sign of the chemical potential can be tuned via an AC magnetic field
driving resonantly one of the magnon modes. Finally, we propose NV-center
relaxometry as a method to experimentally test our predictions.
