Strong-coupling non-Markovian quantum thermodynamics of a spin surrounded by a spin-bath

The focus is on understanding the quantum thermodynamics of strongly coupled non-Markovian quantum systems. We consider a non-trivial, non-Markovian model of a central spin surrounded by a spin bath and derive its exact evolution for arbitrary system-bath couplings. The fundamental quantum thermodynamic quantities, such as system and bath internal energies, work, heat, entropy production, and ergotropy, are calculated using the dynamics and original system (bath) Hamiltonian. We further calculate the Hamiltonian of mean force for the model to study its thermal equilibrium properties. We discuss the cost of cutting interaction on and off in the model, which is related to the work - a mismatch between the system and bath internal energies. Further, an interesting observation relevant to the spin bath acting as a charger is made in a scenario where the central spin is envisaged as a quantum battery. The role of a canonical Hamiltonian in calculating the above thermodynamic quantities, a recently developed technique, is also investigated.