  Single-file diffusion is a paradigmatic model for the transport of Brownian
colloidal particles in narrow one-dimensional channels, such as those found in
certain porous media, where the particles cannot cross each other. We consider
a system where a different external uniform potential is present to the right
and left of an origin. For example, this is the case when two channels meeting
at the origin have different radii. In equilibrium, the chemical potential of
the particles are equal, the density is thus lower in the region with the
higher potential, and by definition there is no net current in the system.
Remarkably, a single-file tracer particle initially located at the origin, with
position denoted by $Y(t)$, exhibits an average {\em up-hill} drift toward the
region of {\em highest} potential. This drift has the late time behavior
$\langle Y(t)\rangle= C t^{1/4}$, where the prefactor $C$ depends on the
initial particle arrangement. This surprising result is shown analytically by
computing the first two moments of $Y(t)$ through a simple and
physically-illuminating method, and also via extensive numerical simulations.
