Relaxation to Negative Temperatures in Double Domain Systems

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.