Ergodic and Nonergodic Anomalous Diffusion in Coupled Stochastic Processes

Inspired by problems in biochemical kinetics, we study statistical properties of an overdamped Langevin process whose friction coefficient depends on the state of a similar, unobserved process. Integrating out the latter, we derive the long time behaviour of the mean square displacement. Anomalous diffusion is found. Since the diffusion exponent can not be predicted using a simple scaling argument, anomalous scaling appears as well. We also find that the coupling can lead to ergodic or non-ergodic behaviour of the studied process. We compare our theoretical predictions with numerical simulations and find an excellent agreement. The findings caution against treating biochemical systems coupled with unobserved dynamical degrees of freedom by means of standard, diffusive Langevin descriptions

Nonequilibrium thermodynamics as a gauge theory

We assume that markovian dynamics on a finite graph enjoys a gauge symmetry under local scalings of the probability density, derive the transformation law for the transition rates and interpret the thermodynamic force as a gauge potential. A widely accepted expression for the total entropy production of a system arises as the simplest gauge-invariant completion of the time derivative of Gibbs's entropy. We show that transition rates can be given a simple physical characterization in terms of locally-detailed-balanced heat reservoirs. It follows that Clausius's measure of irreversibility along a cyclic transformation is a geometric phase. In this picture, the gauge symmetry arises as the arbitrariness in the choice of a prior probability. Thermostatics depends on the information that is disposable to an observer; thermodynamics does not.Comment: 6 pages. Non-fatal errors in eq.(6), eq.(26) and eq.(31) have been amende

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

Methods of Conditionally Optimal Forecasting for Stochastic Synergetic CALS Technologies

Problems of optimal, sub- and conditionally optimal filtering and forecasting in product and staff subsystems at the background noise in synergistical organization-technical-economical systems (SOTES) are considered. Nowadays for highly available systems the problems of creation of basic systems engineering principles, approaches and information technologies (IT) for SOTES from modern spontaneous markets at the background inertially going world economics crisis, weakening global market relations at conditions of competition and counteraction reinforcement is very important. Big enterprises need IT due to essential local and systematic economic loss. It is necessary to form general approaches for stochastic processes and parameters estimation in SOTES at the background noises. The following notations are introduced: special observation SOTES (SOTES-O) with own organization-product resources and internal noise as information from special SOTES being enact noise (SOTES-N). Conception for SOTES structure for systems of technical, staff and financial support is developed. Linear, linear with parametric noises and nonlinear stochastic (discrete and hybrid) equations describing organization-production block (OPB) for three types of SOTES with their planning-economical estimating divisions are worked out. SOTES-O is described by two interconnected subsystems: state SOTES sensor and OPB supporting sensor with necessary resources. After short survey of modern modeling, sub- and conditionally optimal filtering and forecasting basic algorithms and IT for typical SOTES are given. Influence of OTES-N noise on rules and functional indexes of subsystems accompanying life cycle production, its filtration and forecasting is considered. Experimental software tools for modeling and forecasting of cost and technical readiness for parks of aircraft are developed

Comment on "Exact results for survival probability in the multistate Landau-Zener model"

We correct the proof of Brundobler-Elser formula (BEF) provided in [2004 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{37} 4069] and continued in Appendix of [2005 \textit{J. Phys. B: At. Mol. Opt. Phys.} \textbf{38} 907]. After showing that some changes of variables employed in these articles are used erroneously, we propose an alternative change of variables which solves the problem. In our proof, we reveal the connection between the BEF for a general $N$-level Landau-Zener system and the exactly solvable bow-tie model. The special importance of the diabatic levels with maximum/minimum slope is emphasized throughout.Comment: 10 page

Absence of skew scattering in two-dimensional systems: Testing the origins of the anomalous Hall effect

We study the anomalous Hall conductivity in spin-polarized, asymmetrically confined two-dimensional electron and hole systems, focusing on skew-scattering contributions to the transport. We find that the skew scattering, principally responsible for the extrinsic contribution to the anomalous Hall effect, vanishes for the two-dimensional electron system if both chiral Rashba subbands are partially occupied, and vanishes always for the two-dimensional hole gas studied here, regardless of the band filling. Our prediction can be tested with the proposed coplanar two-dimensional electron/hole gas device and can be used as a benchmark to understand the crossover from the intrisic to the extrinsic anomalous Hall effect.Comment: 4 pages, 2 figures include

Formation of a National Assessment of the Probability of Investing in Fraudulent ICOs

The study covers such concepts as ICO and IPO, their characteristics, similarities and differences. A national estimate of the probability of investing in fraudulent ICOs has been formed. Also, the work is about comparing the likelihood of investing in fraudulent IPOs and ICO.     Keywords: cryptocurrency, block technology, ICO, IP