Quantum thermodynamics at strong system-reservoir coupling

At the nanoscale, strong system-reservoir interactions are ubiquitous and could play a significant role in the development of nanoscale quantum machines. As a result, a formulation of thermodynamics which is valid in the quantum regime must incorporate the effects of strong system-reservoir couplings. The reaction coordinate (RC) mapping tackles the strong coupling regime by reshaping the system-environment boundary to include a collective degree of freedom from the environment. This results in an enlarged system, which in turn, is weakly coupled to its surroundings, thus allowing the use of weak-coupling tools for simulations. Nevertheless, this approach is limited due to the growing Hilbert space of the extended system, and the lack of analytical insights into the strong coupling regime.

I will present our efforts to push beyond these limitations and develop a general, transparent, and efficient theory for strong coupling thermodynamics. By combining the RC mapping with a polaron transformation, followed by a truncation of the Hamiltonian, we relocate strong coupling effects from the bath into the energy parameters of the system, ending with a computationally tractable expression for an ``effective" Hamiltonian. We exemplified the power of this approach on canonical models for quantum thermalization, quantum heat transport, and energy conversion devices. We showed that the effective Hamiltonian method is numerically accurate and that it gathers analytical insights into strong coupling effects.