  Flow of particles of two different species through a narrow channel with
solely two discrete spatial positions is analyzed with respect to the species'
capability to cooperate or compete for transport. In contrast to mean field
approaches, spatial correlations are explicitly conserved. A strong repulsive
interaction between particles of the same kind and a very attractive channel
imply a strong entanglement of transport of both species. This is reflected by
the magnitude of transition flows in state space which in the extreme case of
perfect coupling are restricted to a cyclic sub space. Entanglement of
transport implies that the species mutually exert entropic forces on each
other. For parallel directed concentration gradients this implies that the
species' ability to cooperate increases with the degree of entanglement. Thus,
the gradient of one species reciprocally induce a higher flow of the other
species when compared to that in its absence. The opposite holds for
antiparallel gradients where species mutually hamper their transport. For a
sufficient strong coupling, the species under the influence of the stronger
concentration gradient drives the other against its gradient, i.e. flow and
gradient of the driven species become antiparallel. Hence, besides the positive
entropy production generated by the driving species a negative component of
entropy production of the driven species emerges. The sources of both, positive
and negative entropy production, can be localized in state space. The stronger
the coupling of transport the higher is the degree of efficiency, i.e. the
amount of negative entropy production on cost of the positive one.
