Minimizing Dissipation via Interacting Environments: Quadratic Convergence to Landauer Bound

We explore the fundamental limits on thermodynamic irreversibility when cooling a quantum system in the presence of a finite-size reservoir. First, we prove that, for any noninteracting n-particle reservoir, the entropy production Σ decays at most linearly with n. Instead, we derive a cooling protocol in which Σ∝1/n^{2}, which is, in fact, the best possible scaling. This becomes possible due to the presence of interactions in the finite-size reservoir, which must be prepared at the verge of a phase transition. We further show numerically that an intermediate scaling of Σ∝1/n^{δ} with δ∈(1,2) can be achieved using a star-network configuration for the reservoir. Our results open the possibility of cooling with a higher energetic efficiency via interacting reservoirs.