Entropy production provides a general way to state the second law of thermodynamics for non-equilibrium scenarios. In open quantum system dynamics, it also serves as a useful quantifier of the degree of irreversibility. In this work we shed light on the relation between correlations, initial preparation of the system and non-Markovianity by studying a system of two harmonic oscillators independently interacting with their local baths. Their dynamics, described by a time-local master equation, is solved to show - both numerically and analytically - that the global purity of the initial state of the system influences the behaviour of the entropy production rate and that the latter depends algebraically on the entanglement that characterise the initial state.
The Rényi and von Neumann entropies of the thermal state in the generalized uncertainty principle (GUP)-corrected single harmonic oscillator system are explicitly computed within the first order of the GUP parameter $α$. While the von Neumann entropy with $α= 0$ exhibits a monotonically increasing behavior in external temperature, the nonzero GUP parameter makes the decreasing behavior of the von Neumann entropy at the large temperature region. As a result, the von Neumann entropy is maximized at the finite temperature if $α\neq 0$. The Rényi entropy $S_γ$ with nonzero $α$ also exhibits simila…
The spreading properties of the stationary states of the quantum multidimensional harmonic oscillator are analytically discussed by means of the main dispersion measures (radial expectation values) and the fundamental entropy-like quantities (Fisher information, Shannon and Rényi entropies, disequilibrium) of its quantum probability distribution together with their associated uncertainty relations. They are explicitly given, at times in a closed compact form, by means of the potential parameters (oscillator strength, dimensionality, $D$) and the hyperquantum numbers $(n_r,μ_1,μ_2,\ldots,μ_{D-1…
Quantum detectors as autonomous machines: assessing the nonequilibrium thermodynamics of information acquisition
University of Malta（马耳他大学）；TU Wien（维也纳工业大学）；Atominstitut, TU Wien（维也纳工业大学原子研究所）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Trinity College Dublin（都柏林三一学院）；School of Physics, Trinity College Dublin（都柏林三一学院物理学院）；King’s College London（伦敦国王学院）；Department of Physics, King’s College London（伦敦国王学院物理系）
In this chapter we shall discuss the recent progresses of information theoretic tools in the context of free and confined harmonic oscillator. Confined quantum systems have provided appreciable interest in areas of physics, chemistry, biology,etc., since its inception. A particle under extreme pressure environment unfolds many fascinating, notable physical and chemical changes. The desired effect is achieved by reducing the spatial boundary from infinity to a finite region. Similarly, in the last decade, information measures were investigated extensively in diverse quantum problems, in both fr…
We investigate a total thermodynamic entropy production rate of an isolated quantum system. In particular, we consider a quantum model of coupled harmonic oscillators in a star configuration, where a central harmonic oscillator (system) is coupled to a finite number of surrounding harmonic oscillators (bath). In this model, when the initial state of the total system is given by the tensor product of the Gibbs states of the system and the bath, every harmonic oscillator is always in a Gibbs state with a time-dependent temperature. This enables us to define time-dependent thermodynamic entropy f…
We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and …
Dynamical aspects of information-theoretic and entropic measures of quantum systems are studied. First, we show that for the time-dependent harmonic oscillator, as well as for the charged particle in certain time-varying electromagnetic fields, the increase of the entropy and dynamics of the Fisher information can be directly described and related. To illustrate these results we have considered several examples for which all the relations take the elementary form. Moreover, we show that the integrals of (geodesic) motion associated with some conformal Killing vectors lead to the Ermakov-Lewis …
It is well-known that entanglement entropy in field theory at its ground state is dominated by an area law term, presenting a similarity to the entropy of black holes. It is interesting to investigate whether this similarity can be extended by showing that gravitational dynamics emerges from the first law of entanglement thermodynamics. Answering this question requires the specification of the modular Hamiltonian. Motivated by the above, we study entanglement in the toy model of harmonic systems lying at any classicalmost state, i.e. any coherent state. We specify explicitly the reduced densit…
We investigate the dynamics of entanglement, uncertainty and mixedness by solving time dependent Schrödinger equation for two-dimensional harmonic oscillator with time dependent frequency and coupling parameter subject to a static magnetic field. We compute the purities (global/marginal) and then calculate explicitly the linear entropy $S_{L}$ as well as logarithmic negativity $\mathcal{N}$ using the symplectic parametrization of vacuum state. We introduce the spectral decomposition to diagonalize the marginal state and get the expression of von Neumann entropy $S_{von}$ and establish its link…
An entanglement-area law for general bosonic harmonic lattice systems
我们表明，熵的纠缠和纠缠的区域相对于其余的一个一般的谐波晶格系统在地面或热状态的规模最多作为该地区的边界面积。严格证明了该面积定律在任意空间维度的非临界调和晶格系统中，对于一般的有限范围调和相互作用、任意形状的区域和非零温度的状态都是成立的。对于最近邻相互作用-对应于Klein-Gordon情况-纠缠度的上界和下界可以明确地为任意形状的区域陈述，概括了[Phys. Rev. Lett. 94，060503（2005）]。在一维情况下，块熵分析的这些高维类似物表明，在一般条件下，可以预期的面积律的纠缠在非临界谐波多体系统。证明利用纠缠理论的方法，以及块带状矩阵的矩阵函数的结果。还考虑了无序系统。此外，我们构造了一类例子，两点相关长度发散，但仍然可以证明面积法成立。最后，我们考虑了经典谐振子系统中经典关联的标度性，并将其与具有修正相互作用的量子晶格系统联系起来。我们简要地评论临界性和面积定律之间的一般关系的熵纠缠。
