  Our theoretical understanding of glassy dynamics is notoriously incomplete,
and it is even more so when the glassy systems are driven out of equilibrium.
An extreme way to drive a system out of equilibrium is to introduce
nonequilibrium dynamics at the microscopic level, e.g., through active forcing
of the constituent particles or by having nonreciprocal interactions among the
particles. While glassy dynamics under active forcing has been studied by many,
the latter nonequilibrium scenario has received little attention. Here, I study
the glassy dynamics of the spherical $p$-spin model for $p\geq 3$ with
antisymmetric interactions, which generalizes reciprocal interactions in 2-body
interactions. The spherical $p$-spin model is an integral tool in the study of
dynamical glass transition, and when antisymmetric interactions are added, I
show analytically and numerically that glassy behavior is generically
suppressed. Moreover, I obtain analytical expressions on the modified dynamical
glass transition point and the Edward-Anderson parameter (i.e., the asymptotic
plateau height value of the spin-spin correlation function) in the small
driving limit.
