Entropy Production in Non-Markovian Collision Models: Information Backflow vs. System-Environment Correlations

Abstract

We investigate the irreversible entropy production of a qubit in contact with an environment modelled by a microscopic collision model in both Markovian and non-Markovian regimes. Our main goal is to contribute to the discussions on the relationship between non-Markovian dynamics and negative entropy production rates. We employ two different types of collision models that do or do not keep the correlations established between the system and the incoming environmental particle, while both of them pertain to their non-Markovian nature through information backflow from the environment to the system. We observe that as the former model, where the correlations between the system and environment are preserved, gives rise to negative entropy production rates in the transient dynamics, the latter one always maintains positive rates, even though the convergence to the steady-state value is slower as compared to the corresponding Markovian dynamics. Our results suggest that the mechanism underpinning the negative entropy production rates is not solely non-Markovianity through information backflow, but rather the contribution to it through established system-environment correlations.

On the role of initial coherence in the spin phase-space entropy production rate

“…Upon a suitable identification of heat and work, this fundamental result can be recovered in the quantum regime, provided that one considers the standard Born-Markov scenario, as first rigorously shown by Spohn [14]. In contrast, if the system's dynamics is resolved on a timescale such that non-Markovian effects cannot be completely washed out, there might be time intervals in which the entropy production rate gets negative values [15][16][17][18][19]. As counter-intuitive as it might seem at first glance, this occurrence can be framed in the picture of non-Markovianity as backflow of information: in the usual system-environment scenario, the system can partially recover the information that was previously lost due to its interaction with a much larger environment [20][21][22].…”

Charging a quantum battery in a non-Markovian environment: a collisional model approach

“…In the first instance, one could for example look at dephasing, where non-trivial thermodynamic behaviour has recently been found [53]. Concerning non-Markovianity, one could consider collisional models exhibiting information backflow with or without system-environment correlations [54]: it has been indeed shown how the two scenarios have an impact on thermodynamic properties, such as the entropy production rate [55]. These results suggest that it may be interesting to exploit these models in order to further study the actual relationship between ergotropy, decoherence, information backflow and system-environment correlations.…”