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arXiv:2606.05904

Non-equilibrium quantum thermodynamics of a memory-bearing open-system process

Biagio G. Banigi, Eric Lutz, Mauro Paternostro

quant-phSubmitted Jun 4, 2026• Announced Jun 5, 2026• 0 citations
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Abstract

We show the emergence of memory effects in the dynamics of a driven two-level system interacting with a composite environment, and analyze their influence on work, heat and entropy production. We further investigate how the interplay between driving, dissipation and memory effects, stemming from the finiteness of the environment, shapes the thermodynamic response of the system, thus providing insight into quantum thermodynamics beyond the Markovian approximation.

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7 + 4 pages, 7 figures. Comments are welcome!

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We show the emergence of memory effects in the dynamics of a driven two-level system interacting with a composite environment, and analyze their influence on work, heat and entropy production. We further investigate how the interplay between driving, dissipation and memory effects, stemming from the finiteness of the environment, shapes the thermodynamic response of the system, thus providing insight into quantum thermodynamics beyond the Markovian approximation.
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How quantum coherence influences thermodynamic behavior remains an open question in quantum thermodynamics. Here we investigate this relation within the pure dephasing framework, where a central qubit interacts with a finite Ising-like spin environment. Although the system's internal energy remains constant, the interaction induces decoherence and gives rise to nontrivial thermodynamic features. Within the two-point measurement approach, we show that the heat dissipated into the environment matches the coherent energy contribution appearing in a reformulated first law of quantum thermodynamics. Numerical calculations reveal oscillatory coherence dynamics, with revivals associated with information backflow and non-Markovian effects, as quantified by the Breuer-Laine-Piilo measure. We find that heat and coherence exhibit intertwined temporal behavior, with enhanced heat dissipation during coherence decay and reduced heat during revivals. These results suggest a connection between coherence dynamics and thermodynamic quantities in finite, closed composite systems undergoing pure dephasing.
Control of open quantum systems is an essential ingredient to the realization of contemporary quantum science and technology. We demonstrate such control by employing a thermodynamically consistent framework, taking into account the fact that the drive can modify the interaction with environment. Such an effect is incorporated within the dynamical equation, leading to control dependent dissipation, this relation serves as the key element for open system control. Thermodynamics of the control process is reflected by a unidirectional flow of energy to the environment resulting in large entropy production. The control paradigm is displayed by analyzing entropy changing state to state transformations, such as heating and cooling. In addition, the generation of quantum gates under dissipative conditions is demonstrated for both non-unitary reset maps with complete memory loss and a universal set of single and double qubit unitary gates.
We investigate the dynamic evolution and thermodynamic process of a driven quantum system immersed in a finite-temperature heat bath. A Born-Markovian quantum master equation is formally derived for the time-dependent system with discrete energy levels. This quantum master equation can be applied to situations with a broad range of driving speeds and bath temperatures and thus be used to study the finite-time quantum thermodynamics even when nonadiabatic transition and dissipation coexist. The dissipative Landau-Zener model is analyzed as an example. The population evolution and transition probability of the model reveal the importance of the competition between driving and dissipation beyond the adiabatic regime. Moreover, local maxima of irreversible entropy production occur at intermediate sweep velocity and finite temperature, which the low-dissipation model cannot describe.
In this Thesis various aspects of memory effects in the dynamics of open quantum systems are studied. We develop a general theoretical framework for open quantum systems beyond the Markov approximation which allows us to investigate different sources of memory effects and to develop methods for harnessing them in order to realise controllable open quantum systems. \n \nIn the first part of the Thesis a characterisation of non-Markovian dynamics in terms of information flow is developed and applied to study different sources of memory effects. Namely, we study nonlocal memory effects which arise due to initial correlations between two local environments and further the memory effects induced by initial correlations between the open system and the environment. \n \nThe last part focuses on describing two all-optical experiment in which through selective preparation of the initial environment states the information flow between the system and the environment can be controlled. In the first experiment the system is driven from the Markovian to the non- Markovian regime and the degree of non-Markovianity is determined. In the second experiment we observe the nonlocal nature of the memory effects and provide a novel method to experimentally quantify frequency correlations in photonic environments via polarisation measurements.
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.