  Spin-boson Hamiltonians are an effective description for numerous quantum
many-body systems such as atoms coupled to cavity modes, quantum
electrodynamics in circuits and trapped ion systems. While reaching the limit
of strong coupling is possible in current experiments, the understanding of the
physics in this parameter regime remains a challenge, especially when disorder
and dissipation are taken into account. Here we investigate a regime where the
many-body spin dynamics can be related to a Ising energy function defined in
terms of the spin-boson couplings. While in the coherent weak coupling regime
it is known that an effective description in terms of spin Hamiltonian is
possible, we show that a similar viewpoint can be adopted in the presence of
dissipation and strong couplings. The resulting many-body dynamics features
approximately thermal regimes, separated by out-of-equilibrium ones in which
detailed balance is broken. Moreover, we show that under appropriately chosen
conditions one can even achieve cooling of the spin degrees of freedom. This
points towards the possibility of using strongly coupled dissipative spin-boson
systems for engineering complex energy landscapes together with an appropriate
cooling dynamics.
