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.
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.
Abstract We investigate non-Markovianity and its effects on thermodynamic principles and quantum battery performance within a structured nonequilibrium environment consisting of a three-level memory unit and two thermal reservoirs. We demonstrate that temperature imbalance, average temperature, and memory structure serve as effective control parameters for modulating non-Markovianity, exhibiting distinct behaviors for bosonic and fermionic reservoirs. An improved Landauer’s bound applicable to non-Markovian processes is derived, overcoming the limitations of its conventional counterpart. By treating the central system as a quantum battery and the environment as a charger, we show that steady-state ergotropy can be achieved and tuned via thermodynamic parameters. Furthermore, non-Markovian dynamics significantly delay the discharge of the battery. Our study provides a pathway for constructing non-Markovian thermodynamic environments and harnessing non-Markovian effects to enhance the performance of quantum thermal devices.
Controlling the non-Markovian dynamics of open quantum systems is essential in quantum information technology since it plays a crucial role in preserving quantum memory. Albeit in many realistic scenarios the quantum system can simultaneously interact with composite environments, this condition remains little understood, particularly regarding the effect of the coupling between environmental parts. We analyze the non-Markovian behavior of a qubit interacting at the same time with two coupled single-mode cavities which in turn dissipate into memoryless or memory-keeping reservoirs. We show that increasing the control parameter, that is the two-mode coupling, allows for triggering and enhancing a non-Markovian dynamics for the qubit starting from a Markovian one in the absence of coupling. Surprisingly, if the qubit dynamics is non-Markovian for the zero control parameter, increasing the latter enables multiple transitions from non-Markovian to Markovian regimes. These results hold independently on the nature of the reservoirs. This work highlights that suitably engineering the coupling between parts of a compound environment can efficiently harness the quantum memory, stored in a qubit, based on non-Markovianity.
We study the validity of the Landauer principle in the non-Markovian regime by means of collisional models where the intracollisions inside the reservoir cause memory effects generating system-environment correlations. We adopt the system-environment correlations created during the dynamical process to assess the effect of non-Markovianity on the Landauer principle. Exploiting an exact equality for the entropy change of the system, we find the condition for the violation of the Landauer principle, which occurs when the established system-environment correlations become larger than a threshold. We then generalize the study to the nonequilibrium situation where the system is surrounded by many reservoirs at different temperatures. Our results, verified through collisional models with Heisenberg-type interactions, suggest that the complexity of the environment does not play a significant role in the qualitative mechanisms underlying the violation of the Landauer principle under non-Markovian processes.
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.
We study the dynamics of a spin-1/2 particle interacting with a multi-spin environment, modelling the corresponding open system dynamics through a collision-based model. The environmental particles are prepared in individual thermal states, and we investigate the effects of a distribution of temperatures across the spin environment on the evolution of the system, particularly how thermalisation in the long-time limit is affected. We study the phenomenology of the heat exchange between system and environment and consider the information-to-energy conversion process, induced by the system–environment interaction and embodied by the Landauer principle. Furthermore, by considering an interacting-particles environment, we tune the dynamics of the system from an explicit Markovian evolution up to a strongly non-Markovian one, investigating the connections between non-Markovianity, the establishment of system–environment correlations, and the breakdown of the validity of Landauer principle.
The dynamical role of system-environment correlations will lead to the violation of Landauer's principle and may result in a non-Markovian dynamics of the system. Here, we employ entropic quantities called the telescopic relative entropy, to detect non-Markovianity [N. Megier, Phys. Rev. Lett. 127, 030401 (2021)], and study the relation between information backflow of non-Markovian dynamics and the validity of Landauer's principle. We consider a class of energy-conserving system-environment interactions in qubit systems, and we prove that the violation of Landauer's principle corresponds to information backflow of a thermalizing process without coherence and vice versa. Then we study the effect of quantum coherence of the system on the relationship between non-Markovianity and Landauer's principle, and we find that coherence will break the corresponding relation in the information backflow and violation of Landauer's principle. Based on this, we explain the physical mechanism of non-Markovianity in this irreversible process of heat dissipation and information erasure. We further numerically confirm the above theoretical results by means of a collision model.