  Close to equilibrium, the exchange of particles and heat between macroscopic
systems at different temperatures and different chemical potentials is known to
be governed by a matrix of transport coefficients which is positive and
symmetric. We investigate the amounts of heat and particles that are exchanged
between two small quantum systems within a given time, and find them
characterized by a transport matrix which neither needs to be symmetric nor
positive. At larger times even spontaneous transport can be observed in the
total absence of temperature and chemical potential differences provided that
the two systems are different in size. All these deviations from standard
transport behavior can be attributed to the fact that work is done on the
system in the processes contacting and separating those parts of the system
that initially possess different temperatures and chemical potentials. The
standard transport properties are recovered for vanishing work and also in the
limit of large systems and sufficiently large contact times. The general
results are illustrated by an example.
