Entropy

Dynamics of Entropy Production Rate in Two Coupled Bosonic Modes Interacting with a Thermal Reservoir

Tatiana Mihaescu, Аурелиан Исар

Published May 14, 2022• 6 citations

Abstract

The Markovian time evolution of the entropy production rate is studied as a measure of irreversibility generated in a bipartite quantum system consisting of two coupled bosonic modes immersed in a common thermal environment. The dynamics of the system is described in the framework of the formalism of the theory of open quantum systems based on completely positive quantum dynamical semigroups, for initial two-mode squeezed thermal states, squeezed vacuum states, thermal states and coherent states. We show that the rate of the entropy production of the initial state and nonequilibrium stationary state, and the time evolution of the rate of entropy production, strongly depend on the parameters of the initial Gaussian state (squeezing parameter and average thermal photon numbers), frequencies of modes, parameters characterising the thermal environment (temperature and dissipation coefficient), and the strength of coupling between the two modes. We also provide a comparison of the behaviour of entropy production rate and Rényi-2 mutual information present in the considered system.

DOI: 10.3390/e24050696

Related papers

Coherence Dynamics of Two Interacting Bosonic Modes in a Thermal Environment

Аурелиан Исар

We describe the time evolution of the quantum coherence in an open system consisting of two coupled bosonic modes embedded in a thermal reservoir. We discuss the influence of the environment in terms of the covariance matrix for initial squeezed thermal states. The coherence is quantified using the relative entropy as a measure, and its dynamics is studied in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that the evolution of the quantum coherence strongly depends on the initial state of the system (squeezing parameter and thermal photon numbers), the parameters characterizing the thermal reservoir (temperature and dissipation coefficient) and the intensity of the coupling between the two modes.

EPJ Web of ConferencesJan 1, 20200 citations

Entanglement Generation in Two-Mode Gaussian Systems in a Thermal Environment

Аурелиан Исар

We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.

Open Systems & Information DynamicsMar 1, 201616 citations

Evolution of Gaussian Rényi-2 quantum correlations in a squeezed thermal environment

Madalin Calamanciuc, Аурелиан Исар

In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.

International Journal of Quantum InformationJan 21, 20222 citations

Quantum Discord of Two Bosonic Modes in Two-Reservoir Model

Аурелиан Исар

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed vacuum state, we analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. For an initial separable pure state, the Gaussian quantum discord is zero and it keeps this value during the whole evolution of the system.

Open Systems & Information DynamicsSep 1, 201312 citations

Geometric versus Entropic Gaussian Correlations in an Open Quantum System of Two Bosonic Modes

Alina Stoica, Аурелиан Исар

Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification of total nonclassical correlations of Gaussian states. We consider the special case when the initial squeezed thermal state of the system preserves its form in time. We show that time evolution of the measures strongly depends on the parameters characterising the initial state of the system (squeezing parameter and average thermal photon numbers of the two modes) and of the thermal environment (temperature of the thermal bath and dissipation rate). In the limit of large times all the considered measures asymptotically tend to zero value, corresponding to an asymptotic bimodal uncorrelated product state. We make a comparison between the behaviour of the evolution in time of the Gaussian geometric quantum correlations and Gaussian entropic quantum correlations.

Open Systems & Information DynamicsDec 1, 20232 citations

Generation of Gaussian quantum discord of two bosonic modes in a thermal environment

Tatiana Mihaescu, Аурелиан Исар

We describe the time evolution of the Gaussian quantum discord of two coupled bosonic modes interacting with a thermal environment, in the framework of the theory of open quantum systems based on completely positive dynamical semigroups. For initial uni-modal squeezed states the generation of Gaussian discord takes place, for all non-zero values of the strength of interaction between the bosonic modes. After reaching some maximum value in the case of initial uni-modal squeezed states, and also for initial squeezed vacuum states with non-zero Gaussian discord, this measure of quantum correlations non-monotonically decreases in time and tends asymptotically for large times to some definite non-zero value.

AIP conference proceedingsJan 1, 20170 citations