  We study the diffusion of a tracer particle driven out-of-equilibrium by an
external force and traveling in a dense environment of arbitrary density. The
system evolves on a discrete lattice and its stochastic dynamics is described
by a master equation. Relying on a decoupling approximation that goes beyond
the naive mean-field treatment of the problem, we calculate the fluctuations of
the position of the tracer around its mean value on a lattice of arbitrary
dimension, and with different boundary conditions. We reveal intrinsically
nonequilibrium effects, such as enhanced diffusivity of the tracer induced both
by the crowding interactions and the external driving. We finally consider the
high-density and low-density limits of the model and show that our
approximation scheme becomes exact in these limits.
