  Zero-range processes with decreasing jump rates are known to exhibit
condensation, where a finite fraction of all particles concentrates on a single
lattice site when the total density exceeds a critical value. We study such a
process on a one-dimensional lattice with periodic boundary conditions in the
thermodynamic limit with fixed, super-critical particle density. We show that
the process exhibits metastability with respect to the condensate location,
i.e. the suitably accelerated process of the rescaled location converges to a
limiting Markov process on the unit torus. This process has stationary,
independent increments and the rates are characterized by the scaling limit of
capacities of a single random walker on the lattice. Our result extends
previous work for fixed lattices and diverging density in [J. Beltran, C.
Landim, Probab. Theory Related Fields, 152(3-4):781-807, 2012], and we follow
the martingale approach developed there and in subsequent publications. Besides
additional technical difficulties in estimating error bounds for transition
rates, the thermodynamic limit requires new estimates for equilibration towards
a suitably defined distribution in metastable wells, corresponding to a typical
set of configurations with a particular condensate location. The total exit
rates from individual wells turn out to diverge in the limit, which requires an
intermediate regularization step using the symmetries of the process and the
regularity of the limit generator. Another important novel contribution is a
coupling construction to provide a uniform bound on the exit rates from
metastable wells, which is of a general nature and can be adapted to other
models.
