We consider a bipartite quantum conductor and discuss the joint probability distribution of a particle number in a subsystem and the self-information associated with the reduced density matrix of the subsystem. By extending the multicontour Keldysh Green-function technique, we calculate the R\'enyi entropy of a positive integer order
M subjected to the particle number constraint, from which we derive the joint probability distribution. For energy-independent transmission, we derive the time dependence of the accessible entanglement entropy, or the conditional entropy. We analyze the joint probability distribution for energy-dependent transmission probability at the steady state under the coherent resonant tunneling and the incoherent sequential tunneling conditions. We also discuss the probability distribution of the efficiency, which measures the information content transferred by a single electron.
We present a compact and self-contained review of the recently developed Keldysh formalism for multiple parallel worlds. The formalism has been applied to consistent quantum evaluation of the flows of informational quantities, in particular, to the evaluation of Renyi and Shannon entropy flows. We start with the formulation of the standard and extended Keldysh techniques in a single world in a form convenient for our presentation. We explain the use of Keldysh contours encompassing multiple parallel worlds. In the end, we briefly summarize the concrete results obtained with the method.
Using a Wigner-function-based approach, we study the Renyi entropy of a subsystem
A of a system of bosons interacting with a local repulsive potential. The full system is assumed to be in thermal equilibrium at a temperature
T and density $\ensuremath{\rho}$. For a
U(N)-symmetric model, we show that the Renyi entropy of the system in the large-
N limit can be understood in terms of an effective noninteracting system with a spatially varying mean field potential, which has to be determined self-consistently. The Renyi entropy is the sum of two terms: (a) the Renyi entropy of this effective system and (b) the difference in thermal free energy between the effective system and the original translation-invariant system, scaled by
T. We determine the self-consistent equation for this effective potential within a saddle-point approximation. We use this formalism to look at one- and two-dimensional Bose gases on a lattice. In both cases, the potential profile is that of a square well, taking one value in subsystem
A and a different value outside it. The potential varies in space near the boundary of subsystem
A on the scale of density-density correlation length. The effect of interaction on the entanglement entropy density is determined by the ratio of the potential barrier to the temperature and peaks at an intermediate temperature, while the high- and low-temperature regimes are dominated by the noninteracting answer.
Abstract Information entropies, such as Rényi, Fisher, and Shannon, are calculated for the 1s 2 -state of the two-electron series, in position space. It is considered that the exponential cosine screened Coulomb potential (ECSCP) describes the medium. Explicit correlated Hylleraas functions with 3-parameter are used to focus on getting the most distinctive physical features of the inter-electronic repulsion results. In one- and two-electron charge densities, the numerical values of the information entropies and their ratios are calculated. Fisher-Shannon, and Fisher-Rényi information products that measure the electron-electron correlation strength, are calculated and discussed. Also, we used the contour maps and 3D-graphs to visualize how the interplay between inter-electronic repulsion and electrons-nuclear charge interaction determines the variation of information entropies as a function of the nuclear charge and the screening parameter. In this work, an expression for the divergence in Hylleraas coordinates has been derived and the results of the information quantities for two-electron systems with ECSCP have been calculated, in one-and two-electron densities, for the first time.
A probability distribution encodes all the statistics of its corresponding random variable, hence it encodes all one can learn about the system via the random variable. In the theoretical part of this thesis, we discuss several equivalent representations of probability distributions in physics which establishes their roles as complete information measures in their own contexts. In particular, we show how Rényi entropies (as well as relative Rényi entropies) completely characterise the uncertainty of a system, hence implies the insufficiency of Shannon entropy (as well as relative entropy) in capturing the information in the presence of strong fluctuation. We also generalise Jarzynski equality in terms of relative Rényi entropies and show the equivalence between the generalised equality and the work distribution. As a consequence, an equivalence between a monotonic property of relative Rényi entropies and a kind of second law relations is revealed. In the experimental part, we study the non-equilibrium dynamics of an optically levitated nanosphere system in Knudsen regime and discover that, even though the system is not in equilibrium, the dynamics can still be treated as a Brownian motion with an effective temperature and an effective coefficient. Due to the Gaussian statistics of the levitated sphere, we show how some relevant non-equilibrium properties of the system, including several local temperatures, can be analysed from its power spectrum.
We calculate analytically the entanglement and Renyi entropies, the negativity and the mutual information together with all the density and many-particle correlation functions for free bosons on a lattice in the ground state. We show that those quantities can be derived from a multinomial form of the reduced density matrix in the configuration space whose diagonal elements dictate the statistics of the particle distribution, while the off-diagonal coherence terms control the quantum fluctuations. We clarify by this analysis how to reconcile the logarithmic behavior of the entanglement entropy with the volume law of the particle number fluctuations.