Internal conversion of the anionic GFP chromophore: in and out of the I-twisted S1/S0 conical intersection seam

The Z–E photoisomerization quantum yield of the HBDI− chromophore is a result of early, non-statistical dynamics around a less reactive I-twisted intersection and later, statistical behavior around the more reactive, near-enantiomeric counterpart.

Kurtosis of von Neumann entanglement entropy

In this work, we study the statistical behavior of entanglement in quantum bipartite systems under the Hilbert-Schmidt ensemble as assessed by the standard measure - the von Neumann entropy. Expressions of the first three exact cumulants of von Neumann entropy are known in the literature. The main contribution of the present work is the exact formula of the corresponding fourth cumulant that controls the tail behavior of the distribution. As a key ingredient in deriving the result, we make use of what we refer to as unsimplifiable summation bases leading to a complete cancellation. In addition to providing further evidence of the conjectured Gaussian limit of the von Neumann entropy, the obtained formula also provides an improved finite-size approximation to the distribution.

The Transition to Equilibrium in a System with Gravitationally Interacting Particles. I. Temperature Relaxation

The distribution function of systems in equilibrium must have the canonical form of the Gibbs distribution. To substantiate this behavior of systems, attempts have been made for more than 100 years to involve their mechanical behavior. In other words, it seems that a huge number of particles of the medium as a result of interaction with each other according to dynamic laws, is able to explain the statistical behavior of systems during their transition to equilibrium. Modeling of gravitationally interacting particles is carried out and it is shown that in this case, the distribution function does not evolve to the canonical form. Earlier, the same results were obtained for classical Coulomb plasma. On the other hand, such a statistical effect as relaxation is well described by the dynamic behavior of the system, and the simulation data are in agreement with the known theoretical results obtained in various statistical approaches.

Riemannian submersions for q-entropies

In an attempt to find the dynamical foundations for [Formula: see text]-entropies, we examine the special case of Lagrangian/Hamiltonian systems of many degrees of freedom whose statistical behavior is conjecturally described by the [Formula: see text]-entropic functionals. We follow the spirit of the canonical ensemble approach. We consider the system under study as embedded in a far larger total system. We explore some of the consequences that such an embedding has, if it is modeled by a Riemannian submersion. We point out the significance in such a description of the finite-dimensional Bakry–Émery Ricci tensor, as a local mesoscopic invariant, for understanding the collective dynamical behavior of systems described by the [Formula: see text]-entropies.

Statistical Behavior of Lepton Pair Spectrum in the Drell-Yan Process and Signal from Quark-Gluon Plasma in High-Energy Collisions

We analyze the transverse momentum ( p T ) spectra of lepton pairs ( ℓ ℓ ¯ ) generated in the Drell-Yan process, as detected in proton-nucleus (pion-nucleus) and proton-(anti)proton collisions by ten collaborations over a center-of-mass energy s N N or s if in a simplified form) range from ~ 20 GeV to above 10 TeV. Three types of probability density functions (the convolution of two Lévy-Tsallis functions, the two-component Erlang distribution, and the convolution of two Hagedorn functions) are utilized to fit and analyze the p T spectra. The fit results are approximately in agreement with the collected experimental data. Consecutively, we obtained the variation law of related parameters as a function of s and invariant mass Q . In the fit procedure, a given Lévy-Tsallis (or Hagedorn) function can be regarded as the probability density function of transverse momenta contributed by a single quark ( q ) or anti-quark ( q ¯ ). The Drell-Yan process is then described by the statistical method.

Improving the estimation of the COVID-19 effective reproduction number using nowcasting

As the interactions between people increases, the impending menace of COVID-19 outbreaks materializes, and there is an inclination to apply lockdowns. In this context, it is essential to have easy-to-use indicators for people to employ as a reference. The effective reproduction number of confirmed positives, Rt, fulfills such a role. This document proposes a data-driven approach to nowcast Rt based on previous observations’ statistical behavior. As more information arrives, the method naturally becomes more precise about the final count of confirmed positives. Our method’s strength is that it is based on the self-reported onset of symptoms, in contrast to other methods that use the daily report’s count to infer this quantity. We show that our approach may be the foundation for determining useful epidemy tracking indicators.