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.

中文翻译：

---

复合热环境中的非马尔可夫性和Landauer原理

我们研究了一个复合热环境中的非马尔可夫性和Landauer原理，该环境由耗散到马尔可夫水库的记忆组成。关于环境的两个部分的四种不同组合，我们分别考虑了非马尔可夫性，它们分别由量子谐波振荡器和量子位表示，它们具有玻色子和费米子性质。发现通过增加以不同组合为条件的环境温度可以抑制，保持不变性或增强非马尔可夫性。围绕我们的模型，我们建立了一个修正的Landauer原理，该原理适用于非马尔可夫过程。然后，我们将模型推广到具有多个环境的案例，以探索环境对非马尔可夫性的缩放效应。我们发现可以通过扩大环境的大小来增加非马尔可夫性。我们还导出了在这些多个非马尔可夫热环境中的Landauer界。我们的结果提供了在热环境中获取和增强非马尔可夫性的策略，并显示了将常规Landauer原理推广到非马尔可夫过程的可能性。