A Review of Shannon and Differential Entropy Rate Estimation

In this paper, we present a review of Shannon and differential entropy rate estimation techniques. Entropy rate, which measures the average information gain from a stochastic process, is a measure of uncertainty and complexity of a stochastic process. We discuss the estimation of entropy rate from empirical data, and review both parametric and non-parametric techniques. We look at many different assumptions on properties of the processes for parametric processes, in particular focussing on Markov and Gaussian assumptions. Non-parametric estimation relies on limit theorems which involve the entropy rate from observations, and to discuss these, we introduce some theory and the practical implementations of estimators of this type.

Effective phase noise considerations in magnon based parametric excitations

Magnon-phase is an important entity in the parametric processes involving magnons, yet the general qualitative and quantitative consequences of the phase-noise on nonlinear properties remain far from understood. In the current simulation-based theoretical study, we explore the direct impact the phase-noise has on non-linearity. We use analytical techniques usually employed in the study of hydrodynamics to explain the magnon-based nonlinear phenomena. The behavior of the threshold-field and growth rate of the magnons in the presence of Gaussian phase-noise is analytically predicted. These predictions are verified by micromagnetic simulations. Such results are of crucial importance in the design and engineering of both traditional and futuristic devices.

The Quantum Analysis of Nonlinear Optical Parametric Processes with Thermal Reservoirs

In this paper, employing the stochastic differential equations associated with the normal ordering, the quantum properties of a nondegenerate three-level cascade laser with a parametric amplifier and coupled to a two-mode thermal reservoir are thoroughly analyzed. Particularly, the enhancement of squeezing and the amplification of photon entanglement of the two-mode cavity light are investigated. It is found that the two cavity modes are strongly entangled and the degree of entanglement is directly related to the two-mode squeezing. Despite the fact that the entanglement and squeezing decrease with the increment of the mean photon number of the thermal reservoir, strong amount of these nonclassical properties can be generated for a considerable amount of thermal noise with the help of the nonlinear crystal introduced into the laser cavity. Moreover, the squeezing and entanglement of the cavity radiation enhance with the rate of atomic injection.