  We investigate the relaxation of two collective spins in double domain
system, which are individually coupled to a single bosonic reservoir, by
varying the total number of spins in each domain and their initial spin
configurations. A particularly interesting situation occurs when the spin
domains are set in an antiparallel configuration. Further for an unbalanced
configuration where the number of spins are in the excited state initially is
much greater than that in the ground state, the spin ensemble prepared in the
ground state relaxes towards a negative-temperature state.
