  For short-range interacting systems, no Schr\"odinger cat state can be stable
when their environment is in thermal equilibrium. We show, by studying a chain
of two-level systems with nearest-neighbour Ising interactions, that this is
possible when the surroundings consists of two heat reservoirs at different
temperatures, or of a heat reservoir and a monochromatic field. The asymptotic
state of the considered system can be a pure superposition of mesoscopically
distinct states, the all-spin-up and all-spin-down states, at low temperatures.
The main feature of our model leading to this result is the fact that the
Hamiltonian of the chain and the dominant part of its coupling to the
environment obey the same symmetry.
