  Instances of negative mobility, where a system responds to a perturbation in
a way opposite to naive expectation, have been studied theoretically and
experimentally in numerous nonequilibrium systems. In this work we show that
Absolute Negative Mobility (ANM), whereby current is produced in a direction
opposite to the drive, can occur around equilibrium states. This is
demonstrated with a simple one-dimensional lattice model with a driven tracer.
We derive analytical predictions in the linear response regime and elucidate
the mechanism leading to ANM by studying the high-density limit. We also study
numerically a model of hard Brownian disks in a narrow planar channel, for
which the lattice model can be viewed as a toy model. We find that the model
exhibits Negative Differential Mobility (NDM), but no ANM.
