  We investigate the non-equilibrium evolution of ideal Brownian particles
confined between two walls, following simultaneous quenches of the temperature
and a constant external force. We compute (analytically and in numeric
simulations) the post-quench dynamics of the density and the pressure exerted
by the particles on the two walls perpendicular to the drift force. For
identical walls, symmetry breaking associated with the drift gives rise to
unequal particle densities and pressures on the two walls. While the pressure
on one wall increases monotonically after the quench, on the other wall,
depletion causes a non-monotonic dynamics with an overshooting at finite times,
before the long-term steady-state value is reached. For walls immersed in a
Brownian gas, the effective interaction force changes sign from repulsive at
short times to attractive at late times. These findings have potential
applications in various soft matter systems or fluids with charged Brownian
particles, as well as carrier dynamics in semiconducting structures.
