We introduce a tool for the quantitative characterization of the departure from Markovianity of a given dynamical process. Our tool can be applied to a generic N-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its predictive power by tackling a few canonical examples

We investigate the link between information and thermodynamics embodied by Landauer's principle in the open dynamics of a multipartite quantum system. Such irreversible dynamics is described in terms of a collisional model with a finite temperature reservoir. We demonstrate that Landauer's principle holds, for such a configuration, in a form that involves the flow of heat dissipated into the environment and the rate of change of the entropy of the system. Quite remarkably, such a principle for heat and entropy power can be explicitly linked to the rate of creation of correlations among the elements of the multipartite system and, in turn, the non-Markovian nature of their reduced evolution. Such features are illustrated in two exemplary cases.Logical irreversibility and heat dissipation are linked through the relation provided in 1961 by Landauer [1]: the erasure of information on the state of a system is concomitant with the dissipation of heat into the surroundings. In turn, such heat is lower-bounded by a change in the informationtheoretic entropy of the system. Landauer's principle, which has been recently tested [3], was the building block of remarkable advances in our understanding of thermodynamics and its links with logical irreversibility and information theory [2].Recent progress in the quantum approach to nonequilibrium statistical mechanics [4,5] has made the tracking of quantities such as heat, work, and entropy possible in an experimentally viable way. In turn this has enabled the test-bed demonstration of the link between information and energy in quantum systems subjected to elementary quantum computation protocols [6]. The relation between information and the thermodynamic costs of quantum operations has been extensively addressed in the recent past. Noticeable examples include Refs. [7], (cf.[8] for a recent overview). Techniques of quantum statistical mechanics have been used to prove that a finite-size environment can provide tighter bounds to the heat generated in an erasure process [9,10]. The validity of Landauer's principle has been verified for a quantum harmonic oscillator strongly coupled to a bath of bosonic modes [11]. However, such conceptual and experimental progress has not yet resulted in a satisfactory microscopic quantum framework able to account for the emergence of Landauer's principle.In this Letter we provide a derivation of a Landauer-like principle that addresses the heat and entropy fluxes implied in an erasure process described by a collision-based picture of open-system dynamics [12]. Such a microscopic formulation has been used to examine the process of thermalization of a quantum system in contact with a non-zero temperature bath and to investigate the link between with nonMarkovianity and quantum correlations [13][14][15]. Here, we bring together these two perspectives: We analyse the process of information-to-energy conversion in collisional models that make use of general, non-restrictive assumptions and effective mechanisms to describe the heat dissipation into a...

A collision model (CM) is a framework to describe open quantum dynamics. In its memoryless version, it models the reservoir R as consisting of a large collection of elementary ancillas: the dynamics of the open system S results from successive collisions of S with the ancillas of R. Here, we present a general formulation of memoryless composite CMs, where S is partitioned into the very open system under study S coupled to one or more auxiliary systems {S i }. Their composite dynamics occurs through internal S−{S i } collisions interspersed with external ones involving {S i } and the reservoir R. We show that important known instances of quantum non-Markovian dynamics of S-such as the emission of an atom into a reservoir featuring a Lorentzian, or multi-Lorentzian, spectral density or a qubit subject to random telegraph noise-can be mapped on to such memoryless composite CMs.