  We discuss the two-dimensional motion of a Brownian particle that is confined
to a harmonic trap and driven by a shear flow. The surrounding medium induces
memory effects modelled by a linear, typically nonreciprocal coupling of the
particle coordinates to an auxiliary (hidden) variable. The system's behavior
resulting from the microscopic Langevin equations for the three variables is
analyzed by means of exact moment equations derived from the Fokker-Planck
representation, and numerical Brownian Dynamics (BD) simulations. Increasing
the shear rate beyond a critical value we observe, for suitable coupling
scenarios with nonreciprocal elements, a transition from a stationary to an
instationary state, corresponding to an escape from the trap. We analyze this
behavior, analytically and numerically, in terms of the associated moments of
the probability distribution, and from the perspective of nonequilibrium
thermodynamics. Intriguingly, the entropy production rate remains finite when
crossing the stability threshold.
