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.Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. EE , which results in an intermediate case. Finally, the gray, dashed curve is for p = J 4 EE , i.e. a complete Swap, and thus strongly non-Markovian dynamics. The -E coupling constant is p = J 32 E for weak coupling, then b = 1 and the system and environment proper frequencies are w = 3 s and w = 1 e respectively.
We consider the dynamics of a collisional model in which both the system and environment are embodied by spin-1/2 particles. In order to include non-Markovian features in our model we introduce interactions among the environmental qubits and investigate the effect that different models of such interaction have on the degree of non-Markovianity of the system's dynamics. By extending that interaction beyond the nearest-neighbour, we enhance the degree of non-Markovianity in the system's dynamics. A further significant increase can be observed if a collective interaction with the forthcoming environmental qubits is considered. However, the observed degree of non-Markovianity in this case is non-monotonic with the increasing number of qubits included in the interaction. Moreover, one can establish a connection between the degree of non-Markovianity in the evolution of the system and the fading behaviour of quantum coherence in its state as the number of collisions grow. We complement our study with an investigation on system-environment correlations and present an example of their importance on a physical upper bound on the trace distance derivative.PACS numbers: 03.65. Yz, 42.50.Lc The theory of open quantum systems deals with the inevitable interaction between a system and its surrounding environment, which results in a non-unitary time evolution of the system density matrix [1][2][3]. As a result, quantum coherence and the information encoded in the system's state are lost into the environmental degrees of freedom. In the case of a Markovian evolution, the loss of system information is monotonic and at any time the future evolution of the system only depends on its present state. On the other hand, non-Markovian dynamics can be associated with a temporary reverse of such a flow of information, which results in the system regaining some of the lost information and making the future evolution of the system dependent on its past.Recently, the characterization and quantification of non-Markovian dynamics has attracted a lot of attention. The tools of quantum information theory have been used extensively to quantify the amount of information backflow from the environment to the system, thus providing an important intuitive understanding of non-Markovianity [4,5]. The measures of non-Markovianity put forward so far are helping us characterize the features of memory-bearing quantum open-system dynamics, shedding light on the ultimate origins of such behaviours. In general, however, they do not mutually agree on the emergence and degree of non-Markovianity. In this sense, they all characterize it from different perspectives [6].In this work, we consider a model that describes the systemenvironment interaction through a series of sequential "collisions" between the system and the environmental particles. Such "collisional" model is capable of simulating both Markovian and non-Markovian dynamics depending on the interaction and/or correlation between the environmental degrees *
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