We obtain a Gorini-Kossakowski-Sudarshan-Lindblad-like master equation for two or more quantum systems connected locally to a combination of Markovian and non-Markovian heat baths. The master equation was originally formulated for multiparty systems with either exclusively Markovian or non-Markovian environments. We extend it to encompass the case of multiple quantum systems connected to a mixture of Markovian and non-Markovian heat baths. The coexistence of both non-Markovian and Markovian environments is a plausible scenario, particularly when studying hybrid physical systems such as atom-photon arrangements. We analyze the thermodynamic quantities for such a set of local environments, and derive a modified form of the Spohn's theorem for the setup. The modification of the theorem naturally leads to a witness as well as an easily computable quantifier of non-Markovianity. Expectedly, we find that for multiparty situations, where a combination of Markovian and non-Markovian heat baths are active, the response in thermodynamic system characteristics due to non-Markovian baths is prominent at times close to the initial time of evolution, whereas the long-time behavior is predominantly controlled by the Markovian ones.
We obtain a Gorini-Kossakowski-Sudarshan-Lindblad-like master equation for two or more quantum systems connected locally to a combination of Markovian and non-Markovian heat baths. The master equation was originally formulated for multiparty systems with either exclusively Markovian or non-Markovian environments. We extend it to encompass the case of multiple quantum systems connected to a mixture of Markovian and non-Markovian heat baths. The coexistence of both non-Markovian and Markovian environments is a plausible scenario, particularly when studying hybrid physical systems such as atom-photon arrangements. We analyze the thermodynamic quantities for such a set of local environments, and derive a modified form of the Spohn's theorem for the setup. The modification of the theorem naturally leads to a witness as well as an easily computable quantifier of non-Markovianity. Expectedly, we find that for multiparty situations, where a combination of Markovian and non-Markovian heat baths are active, the response in thermodynamic system characteristics due to non-Markovian baths is prominent at times close to the initial time of evolution, whereas the long-time behavior is predominantly controlled by the Markovian ones.
We analyze the exact dynamics of a generalized quantum Brownian motion model, employing Gaussian master equation methods. We demonstrate that, by modulating the relative weights of specific interaction channels, we can control the degree of non-Markovianity of the system, and induce a transition from non-Markovian to Markovian regimes. The non-Markovianity of the evolution is formally characterized by leveraging the Gorini--Kossakowski--Sudarshan--Lindblad theorem and by employing quantitative measures of information backflow. Finally, we clarify the physical mechanism behind the phenomenology of this model, thereby providing a systematic platform for environment engineering through the strategic tuning of dissipation channels.
We investigate the long-time behavior of quantum Markovian dynamics generated by time-dependent Gorini–Kossakowski–Lindblad–Sudarshan (GKLS) master equations. We introduce a notion of weak relaxation and derive sufficient conditions guaranteeing asymptotic independence from the initial state. Our results provide a quantitative extension of the Spohn–Frigerio theorem to time-dependent generators, yielding explicit contraction bounds in terms of the instantaneous steady state and the jump operators. For a class of microscopically derived master equations, we further obtain a graph-theoretic characterization of the aforementioned conditions that directly links the structure of the jump operators to the relaxation properties. The general theory is illustrated by applications to driven finite-level systems, including a detailed three-level example, and is extended to a non-Markovian setting by means of time-local master equations that become of GKLS form at long times. These findings pave the way for the development of a more general theory of relaxation beyond the Markovian case.
For a model of a multilevel system interacting with several baths at zero temperature, it is shown that its dynamics becomes Markovian after the bath correlation time. We take into account not only the contribution of the bath spectral density, which leads to a continuous correlation function, but also the ohmic contribution to the spectral density, which leads to a renormalization of both equations and initial conditions. An explicit Gorini–Kossakowski–Sudarshan–Lindblad equation describing the dynamics of the system after the bath correlation time is derived, and the form of initial conditions for this equation is obtained. They do not coincide with the exact initial conditions due to the renormalization associated with the ohmic contribution and due to the short initial non-Markovian time interval preceding the bath correlation time.
A consistent theory of non-equilibrium thermodynamics for Markovian open quantum systems has been developed in the late seventies in analogy with Classical Irreversible Thermodynamics. The time-evolution of these open systems is usually described by means of effective master equations in Lindblad form, that turn out to be reliable when there is a separation of time-scales between system and environment, such that memory effects are negligible and the so-called Markovian approximation is justified. In this framework, the variations of energy and entropy in the system are consistently described, distinguishing between heat and work contributions and providing a statement of the second law of thermodynamics as positivity of the entropy production.\nHowever, there is empirical evidence that many physical systems like photosynthetic complexes,\nopto-mechanical resonators and superconducting qubits, just to mention a few, experience more general non-Markovian dynamics. The formulation of the laws of thermodynamics in a non-Markovian setting is matter of current research and represents the main topic of the present work. As a first step, we show that the entropy production defined as in the Markovian case can be negative for a class of non-Markovian dynamics. We argue that this outcome should not be interpreted as a violation of the second law of thermodynamics because the environment must be explicitly taken into account in the balance of entropy in the non-Markovian setting. In order to justify this claim we adopt a more general point of view, studying a closed bipartite quantum system, such that each of the two subsystems plays the role of a finite environment out of equilibrium for the other one. We concentrate on the balance of energy first and construct an effective Hamiltonian for each subsystem using physically reasonable requirements; then we define heat and work as in the standard Markovian treatment, with the effective Hamiltonian replacing the free Hamiltonian. It turns out that, in our framework, the work power is perfectly balanced between subsystems, while the correlations can store a part of energy locally inaccessible and exchange it with both subsystems in the form of heat.\nConcerning the balance of entropy, a quite general formulation of the second law of thermodynamics can be given as follows: under the assumption of a factorized initial state for the compound system, the sum of the total variations of the entropies in the two subsystems is always nonnegative. We show with an explicit example that this general formulation does not correspond to the statement presented in the framework of Markovian master equations, which should not be considered a priori the second law of thermodynamics.\nIn the last part of the thesis we concentrate of the so-called fluctuation relations, that are results extending the thermodynamic formalism beyond the behavior of average quantities. After reviewing the main theoretical outcomes, such as the Jarzynski equality and the Crooks fluctuation theorem, we describe a proposal to access experimentally the work performed on an ensemble of diatomic molecules by a time-dependent electric field coupled with their vibrational degree of freedom. This procedure could then be used to test the quantum Jarzynski equality. With respect to the results so far appeared in the literature, in which the left-hand side of the equality is inferred from an experiment and the right-hand side is computed according to a model, in our proposed setting we should be able to estimate from the experiment both the left-hand side and the right-hand side of the equality, independently.
Abstract For a model of a multilevel system interacting with several baths at zero temperature, it is shown that its dynamics becomes Markovian after the bath correlation time. We take into account not only the contribution of the bath spectral density, which leads to a continuous correlation function, but also the ohmic contribution to the spectral density, which leads to a renormalization of both equations and initial conditions. An explicit Gorini–Kossakowski–Sudarshan–Lindblad equation describing the dynamics of the system after the bath correlation time is derived, and the form of initial conditions for this equation is obtained. They do not coincide with the exact initial conditions due to the renormalization associated with the ohmic contribution and due to the short initial non-Markovian time interval preceding the bath correlation time.
A method is proposed to describe Fermi or Bose systems coupled to one or several heat baths composed of fermions and/or bosons. The method, called the coupled equations of motion method, properly includes non-Markovian effects. The approach is exact in the full-coupling approximation when only bosonic particles are present in the system and baths. The approach provides an approximate treatment when fermions are present either in the system and/or in one or several environments. Our approach has the advantage of properly respecting the Pauli exclusion principle for fermions during the evolution. We illustrate the approach for the single fermionic or bosonic oscillator coupled to one or two heat baths assuming different types of quantum statistics (fermion or boson) for them. The cases of a Fermi system coupled to fermion or boson heat baths or a mixture of both are analyzed in detail. With the future goal of treating Fermi systems formed of an increasing number of two-level systems (qubits), we discuss possible simplifications that could be made in the equations of motion and their limits of validity in terms of the system-bath coupling or of the initial heat bath temperatures.