  We study the distribution of active, noninteracting particles over two bulk
states separated by a ratchet potential. By solving the steady-state
Smoluchowski equations in a flux-free setting, we show that the ratchet
potential affects the distribution of particles over the bulks, and thus exerts
an influence of infinitely long range. As we show, crucial for having such a
long-range influence is an external potential that is nonlinear. We
characterize how the difference in bulk densities depends on activity and on
the ratchet potential, and we identify power law dependencies on system
parameters in several limiting cases. While weakly active systems are often
understood in terms of an effective temperature, we present an analytical
solution that explicitly shows that this is not possible in the current
setting. Instead, we rationalize our results by a simple transition state
model, that presumes particles to cross the potential barrier by Arrhenius
rates modified for activity. While this model does not quantitatively describe
the difference in bulk densities for feasible parameter values, it does
reproduce - in its regime of applicability - the complete power law behavior
correctly.
