Non-Markovianity and a generalized Landauer bound for a minimal quantum autonomous thermal machine with a work qubit

We investigate the validity of the Landauer principle in the context of a non-Markovian environment, employing a quantum autonomous thermal machine (QATM) comprised of two qubits, attached to different Markovian thermal reservoirs coupled to a single qubit acting as a quantum coherence reservoir, interpreted as a working qubit. We numerically demonstrate that the non-Markovianity, arising from the exchange of correlations between the QATM qubits and the work qubit, influences the Landauer bound. We analyze two distinct reservoir types: fermionic and bosonic, and show that the QATM, operating as a single entity, interacts with the work qubit at an effective virtual temperature, leading to a violation of the conventional Landauer bound. Consequently, we derive a lower bound for the minimal dissipation energy required to erase information during the energy exchange between the QATM and the work qubit. The QATM's information engine character and impact on the work qubit is further characterized by monitoring its information content, including coherence and population dynamics. Our analysis reveals that the work qubit's populations oscillate in time, while the coherence dissipates nonmonotonically.