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arXiv:2204.09522 · Entropy

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

Hüseyin Talha Şenyaşa, Şahinde Kesgin, Göktuğ Karpat, Barış Çakmak

Published Jun 14, 2022• 9 citations
arXivHTMLPDF

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.

DOI
10.3390/e24060824

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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.
Abstract We consider a microscopic collision model, i.e., a quantum system interacts with a hierarchical environment consisting of an auxiliary system and a reservoir. We show how the non-Markovian character of the system is influenced by the coupling strength of system-auxiliary system and auxiliary system-reservoir, coherence of environment and initial system-environment correlations. And we study the non-Markovianity induced by coherence of environment from the perspective of energy, further the relationship between information backflow and energy flux is obtained. Then we study the effect of non-Markovianity on thermodynamic properties. By studying the entropy change of system especially that from heat exchanges with the environment, we reveal the essence of entropy change between positive and negative values during non-Markovian evolution is due to the contribution of heat flux induced by coherence. And compared with the case of Markovian dynamics, we observe that the entropy production decreases in some specific time intervals under non-Markovian dynamics induced by the coupling strength. And this is different to the case of non-Markovianity caused by initial system-environment correlation, that we show the possibility of positive entropy production during the whole dynamics.
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.
Detuned systems can spontaneously achieve a synchronous dynamics and display robust quantum correlations in different local and global dissipation regimes. Beyond the Markovian limit, information backflow from the environment becomes a crucial mechanism whose interplay with spontaneous synchronization is unknown. Considering a model of two coupled qubits, one of which interacts with a dissipative environment, we show that non-Markovianity is highly detrimental for the emergence of synchronization, for the latter can be delayed and hindered because of the presence of information backflow. The results are obtained considering both a master equation approach and a collision model based on repeated interactions, which represents a very versatile tool to tailor the desired kind of environment.
We study the relationship between (non-)Markovian evolutions, established correlations, and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the system is strongly coupled to an ancillary qubit. We examine the steady-state properties finding that the coupling leads to effective temperatures emerging in the composite system, and show that this is related to the creation of correlations between the qubits. By establishing the conditions under which the system reaches thermal equilibrium with the bath despite undergoing a non-Markovian evolution, we examine the entropy production rate, showing that its transient negativity is a sufficient sign of non-Markovianity.
Entropy production plays a fundamental role in nonequilibrium thermodynamics to quantify the irreversibility of open systems. Its positivity can be ensured for a wide class of setups, but the entropy production rate can become negative sometimes. This is often taken as an indicator of non-Markovianity. We make this link precise by showing under which conditions a negative entropy production rate implies non-Markovianity and when it does not. For a system coupled to a single heat bath, this can be established within a unified language for two setups: (i) the dynamics resulting from a coarse-grained description of a Markovian master equation and (ii) the classical Hamiltonian dynamics of a system coupled to a bath. The quantum version of the latter result is shown not to hold despite the fact that the integrated thermodynamic description is formally equivalent to the classical case. The instantaneous fixed point of a non-Markovian dynamics plays an important role in our study. Our key contribution is to provide a consistent theoretical framework to study the finite-time thermodynamics of a large class of dynamics with a precise link to its non-Markovianity.
We study the relationship between a (non-)Markovian evolution and the entropy production rate. We consider a system qubit in contact with a thermal bath and in addition the system is strongly coupled to an ancillary qubit. We examine the steady state properties finding that the coupling leads to effective temperatures emerging in the composite system, and show that this is related to the creation of correlations between the qubits. By establishing the conditions under which the system reaches thermal equilibrium with the bath despite undergoing a non-Markovian evolution, we examine the entropy production rate, showing that its transient negativity is a sufficient sign of non-Markovianity.