Qi Tan, Peng-Cheng Li

We compute the instantaneous angular momentum flux from nonspinning black hole binaries in Einstein-Maxwell-dilaton theory for generic noncircular orbits up to relative first post-Newtonian order. Working in the Einstein frame and using the direct integration of the relaxed field equations approach, we construct the scalar, electromagnetic, and tensor gravitational fields in the wave zone and express the required source multipole moments in the center-of-mass frame. In addition to the leading $1/R$ radiative fields, we retain the next-to-leading $1/R^2$ terms in the wave-zone fields, which describe finite-distance corrections and do not contribute to the flux at null infinity. We obtain separately the scalar, electromagnetic, and tensor contributions to the angular momentum flux. The scalar and electromagnetic channels begin with dipole radiation, while the tensor channel begins at quadrupole order. Our results recover the quasicircular balance relation, the known general-relativistic limit, and the expected scalar- and electromagnetic-dipole suppression limits. Together with the previously known energy flux, these results provide the dissipative information required for future studies of orbit-averaged eccentric evolution and waveform phasing in Einstein-Maxwell-dilaton theory.