Non-Markovianity and the Landauer principle in composite thermal environments

We study non-Markovianity and the Landauer principle in a composite thermal environment consisting of a memory dissipated to a Markovian reservoir. We consider non-Markovianity with respect to four different combinations of two parts of the environment regarding their bosonic and fermionic natures represented by a quantum harmonic oscillator and a qubit, respectively. It is found that non-Markovianity can be suppressed, kept invariant, or enhanced by increasing environmental temperature conditioned on different combinations. Focusing on our model, we establish a modified Landauer principle which holds in the non-Markovian process. We then generalize the model to the case with multiple environments to explore scaling effects of the environments on non-Markovianity. We find that non-Markovianity can be increased by enlarging the size of the environments. We also derive a Landauer bound in these multiple non-Markovian thermal environments. Our results provide strategies for acquiring and enhancing non-Markoviaity in the thermal environments and show the possibility to generalize the conventional Landauer principle to the non-Markovian process.