arXiv subjects

V. V. Ryazanov

Publications and source records attributed to V. V. Ryazanov.

At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics of the space of trajectories governed by a combination of two additive boundary functionals

This paper extends the formalism of stochastic path-space thermodynamics by systematically expanding the space of thermodynamic variables with a spectrum of boundary and relative functionals of random processes. Generalizing the approaches introduced in preprints arXiv:2607.24078 and arXiv:2609.08477, we investigate the fluctuation statistics of a one-dimensional Ornstein-Uhlenbeck process with an asymmetric linear drift and a step penalty potential at the origin, which models the waiting phase of a molecular Brownian motor. Utilizing the Feynman-Kac formalism and the parabolic cylinder theory, a numerical scheme based on matching logarithmic derivatives via the secant method is constructed. A high-precision eigenvalues of the effective Hamiltonian is obtained, which define the cumulant generating function. We formulate a modified path-space fluctuation theorem of the Gallavotti-Cohen type for the conjugate drift current at a fixed integral occupation time of the system in the dissipative half-plane. The physical and thermodynamic significance of the new variables is elucidated. A combination of "residence time" and "integral current" functionals is applied to describe an ion channel sensitive to mechanical or electrical stimuli.

cond-mat.stat-mech↗

arXiv2026

Nonequilibrium stochastic thermodynamics of boundary functionals: From Zubarev's ensemble to stochastic particle separation

This paper develops a generalization of Zubarev's nonequilibrium statistical operator method for the case of simultaneous inclusion of additive and nonlocal boundary functionals of trajectories. Using a unified thermodynamic approach, a three-parameter model of nonequilibrium systems is constructed, including the first-passage time, the dwell time above a given level, and the absolute extremum of the process. A correspondence is demonstrated between the maximum information entropy method for trajectories and the Donsker-Varadan large deviation formalism. Using the Doob`s h-transform, it is demonstrated that fixing extremal functionals of history induces efficient non-Markovian transport in the system with dynamic adaptation to historical records. Criteria for the applicability of the developed apparatus in the "large time" domain and the possibilities of its use for optimizing stochastic particle separation in periodic potentials are discussed.

cond-mat.stat-mech↗

arXiv2026

Thermodynamics with thermodynamic variable first-passage time. I. From stochastic trajectories to nonlinear transport equations

The theoretical foundation of combining external nonequilibrium thermodynamics, the nonequilibrium statistical operator method, and stochastic first passage time thermodynamics are explored. It is shown that including a random lifetime of a metastable state in the generalized distribution function allows the first passage time to be considered as a fully - fledged macroscopic coordinate. A microscopic justification for this approach is provided, and a generalized thermodynamic potential is introduced. A procedure for closing the transport equations based on on thermodynamic consistency conditions is developed. It is shown that in the generalized Maxwell - Catteneo equation, the classical relaxation time is strictly replaced by the mean first passage time, which imparts internal macroscopic nonlinearity to the system. Using renewal theory, the exact mathematical structure of transport memory kernels for non-Markovian processes is derived. A qualitative comparative analysis of various approaches to the thermodynamic description of nonequilibrium phenomena is presented.

cond-mat.stat-mech↗

arXiv2026

Thermodynamics with thermodynamic variable first-passage time. II. Dynamics of explosive boiling of superheated liquid, critical indices, fractional calculus

Within the framework of stochastic first-passage time thermodynamics (TFPT) and power-law distributions (Mittag-Leffler and Levy), the appearance of fractional Caputo derivatives in hydrodynamic equations is substantiated. The developed framework is applied to the problem of explosive boiling of a superheated liquid: an integral formula for nonlocal entropy production is derived and the critical index of dissipation intensity is calculated, along with qualitative changes in these parameters upon introducing external pressure. It is found that dissipation at a given instant is strictly determined by the integral history of the macroscopic matter flow J(t) over the entire evolutionary interval up to the moment of phase explosion. The calculated critical dissipation index z strictly describes the kinetic catastrophe and the violation of Prigogine's minimum entropy production principle near spinodals.

cond-mat.stat-mech↗

arXiv2026

A stochastic model of a nuclear reactor with directed percolation. Overjump and maximum power

A stochastic risk model is applied to simulating the behavior of a nuclear reactor in a situation where the neutron chain length is described by a distribution with heavy "tails," such as the Pareto distribution. Probabilities of a fluctuation exceeding a critical threshold are obtained, and risk bounds for power-law distributions of jumps are estimated. Functionals of the reactor power maximum, the instant of first reaching the maximum, and the distribution of the overjump magnitude are considered. A relationship between the shape parameter and the physical constants of reactors is obtained, as well as the relationship with the noise spectrum and physical constants. The finite dimensions of a real reactor are taken into account. The autocorrelation function of the truncated Lévy process and its relationship with the frequency filters of the neutron flux monitoring equipment are considered.

cond-mat.dis-nn↗

arXiv2026

Directed percolation in nuclear safety

Neutron behavior in a nuclear reactor is described using a directed percolation model. The preferred direction is created by time-oriented neutron generations. Using the time required to reach a dangerous neutron flux limit or reactor power limit as an example, it is shown that, in certain situations, the proposed approach can detect events hazardous to reactor safety that are undetectable by traditional reactor safety systems. The capabilities and limitations of the proposed approach are outlined.

cond-mat.stat-mech↗

arXiv2026

Stochastic Safety Limits and Scale-Dependent Power Fluctuations in Nuclear Reactors: A Critical Scaling Approach

Applying boundary functionals of random risk processes to various physical problems makes it possible to determine many important characteristics of these problems. For example, a special case of boundary functionals is the time to first reach a level, which is widely and successfully applied to a variety of problems. We consider the application of boundary functionals to solving nuclear safety problems. In situations such as reactor startup, as well as for certain types of reactors, neutron behavior changes. Neutron clustering begins to play an important role, and the distributions characterizing neutron behavior change. The normal Gaussian distribution is replaced by stable limiting, distributions to which the sums of random variables converge. Boundary functionals allow us to accurately calculate the statistics of random events, determine the behavior of reactor power peaks, the probabilities of catastrophic power surges, and other quantities important for reactor safety, providing a mathematical bridge between the abstract theory of directed percolation and engineering calculations of protection parameters. This article examines the first-passage time to reach a certain level.

cond-mat.dis-nn↗

arXiv2026

Possibilities of applying boundary functionals of random processes to nuclear safety problems

The potential for using boundary functionals of random risk processes to solve nuclear safety problems at nuclear power plants is assessed. In certain situations (MSRs (Molten Salt Reactors), High-Temperature Gas-Cooled Reactors (HTGRs), pulverized fuel reactors, reactor startups, and accident analysis (core collapse)), neutron behavior changes significantly. Neutron clustering begins to play an important role, and the distributions characterizing neutron behavior change. The normal distribution is replaced by stable, but also limiting, distributions. Boundary functionals allow for precise calculation of the power quantile and provide a mathematical bridge between abstract directed percolation and engineering calculations of protection settings.

cond-mat.stat-mech↗

arXiv2026

Multifractality, percolation threshold and critical point of a nuclear reactor

A multifractal model is used to analyze neutron evolution within a reactor. For chain reactions, various characteristics of multifractal neutron behavior have been determined. These include the dimension of the multifractal carrier, information and correlation dimensions, the entropy of the fractal set, maximum and minimum dimension values, and the multifractal spectrum function. The geometric features of a multifractal allow for the description of a stochastic system consisting of hierarchically subordinate statistical ensembles, which are characterized by Cayley trees. A stationary distribution over hierarchical levels is established, which follows the Tsallis power law. The text also points out some potential applications of fractal patterns in nuclear reactor theory. The chance of percolation, which is when we see a state in the Bethe lattice where there's at least one continuous path through neighboring conducting nodes all the way across, is similar to the likelihood of a self-sustaining fission chain reaction happening. When this probability hits a critical point, we get a (conditionally) infinite cluster of neutrons forming. The percolation probability, influenced by how long the reactor has been running and its size, is linked to the reactor's criticality. We take a look at how the neutron multiplication factor behaves over time. We especially focus on the early stages of a self-sustaining nuclear fission chain reaction. We also highlight the ways to identify the boundaries of the critical region.

cond-mat.dis-nn↗

arXiv2025

Application of boundary functionals of the theory of random processes to aerosol coagulation

A new approach to describing aerosol behavior is proposed. Boundary functionals of random process theory are applied to describe the behavior of aerosol concentrations during coagulation. It is shown that considering the first-passage time of a given aerosol concentration level corresponds to experimental results for the time dependence of aerosol concentration. Probabilities for aerosol concentrations to attain specific values are obtained, as well as expressions for average aerosol concentrations.

cond-mat.stat-mech↗

arXiv2025

Stochastic storage models in theoretical physics problems

Stochastic storage models based on essentially non-Gaussian noise are considered. The stochastic description of physical systems based on stochastic storage models is associated with generalized Poisson (or shot) noise, in which the jump values can be quite large. Stochastic storage models have a direct physical meaning: some elements enter the system and leave it. Storage processes fit into the general scheme of dynamic systems subject to the additive influence of a random process. The main relationships of storage models are described, and the possibilities of applying the mathematical provisions of stochastic storage processes to various physical problems are indicated. A number of examples of applying the stochastic storage model are considered.

cond-mat.stat-mech↗

arXiv2025

Relation between stochastic processes and thermodynamics of trajectories

The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular, dynamic activity, are considered. A correspondence between expressions of the theory of random processes and thermodynamics of trajectories, as well as deviations from such a correspondence for the process of fluctuations of trajectory observables, are established. The connections between general regularities of first-passage times in the theory of random processes and thermodynamics of trajectories are discussed. A more complete use of the theory of random processes in physical problems is proposed, and the possibilities of combining approaches of the theory of random processes and statistical physics are indicated.

cond-mat.stat-mech↗

arXiv2025

First-Passage Time for Upper Bounds on Fluctuations of Trajectory Observables

General upper bounds on fluctuations of trajectory observables were recently obtained. It turned out that the size of fluctuations of dynamical observable is limited from below and from above. For the moment generating function of general upper bounds on the size of fluctuations, the moments (average value and variance) of the size of fluctuations are obtained. A more complex and interesting task is to obtain the first-passage time for process of upper bounds on the moments and first-passage time (FPT) of the observable A, which are obtained by calculating the moments and FPT of the process of upper bound. Characteristic functions, average values and variances of the first-passage time of reaching fluctuations of observables of the trajectory of the Markov chain of positive and negative levels are also obtained. Some general issues of the relationship between the theory of random processes (using the example of the risk theory used) and thermodynamics of trajectories are also considered.

cond-mat.stat-mech↗

arXiv2025

Application of boundary functionals of random processes in statistical physics

The potential applications of boundary functionals of random processes, such as the extreme values of these processes, the moment of first reaching a fixed level, the value of the process at the moment of reaching the level, the moment of reaching extreme values, the time the process stays above a fixed level, and other functionals, are considered for the description of physical, chemical, and biological problems. Definitions of these functionals are provided, and characteristic functions are presented for the model with an exponential distribution of incoming demands. A generalization of these limitations is also considered. The potential uses of boundary functionals are demonstrated through examples such as a unicyclic network with affinity A, an asymmetric random walk, nonlinear diffusion, two-level model, Brownian motion, and multiple diffusing particles with reversible target-binding kinetics.

cond-mat.stat-mech↗

arXiv2024

Influence of Entropy Changes on First Passage Time in the Thermodynamics of trajectories

An ensemble of trajectories with dynamical activity and first-passage time (FPT) is considered in the context of the thermodynamics of trajectories. The relationship between the average FPT and the total change in entropy is determined, with a focus on non-negative values of the total change in entropy only. Similar dependencies were found for dynamic activity, the dispersion of dynamic activity, and FPT, as well as for the correlation between dynamic activity and FPT. Applying the obtained results to model systems reveals dependencies on entropy changes in stationary nonequilibrium and equilibrium states. To relate changes in entropy to the conjugate parameter of the FPT, three models of the distribution function are applied to classical two- and three-level systems, and to a quantum two-level system.

cond-mat.stat-mech↗

arXiv2024

First passage times of charge transport and entropy change

All real physical processes, including of the first-passage time, occur with a change in entropy. This circumstance is not taken into account when studying the first-passage time, but is illustrated in this article using the example of electron transfer through a metallic double dot. The statistics of the first-passage time of a random process N(t) for electrons transferred through a metallic double dot is considered. The expressions for the average first-passage time are compared with and without taking into account the change in entropy during this time. External influences on the average value of the first-passage time are considered for the case of DC bias voltage.

cond-mat.stat-mech↗

arXiv2024

Comparison of extended irreversible thermodynamics and nonequilibrium statistical operator method with thermodynamics based on a distribution containing the first-passage time

An analogy is drawn between version of non-equilibrium thermodynamics a distribution-based containing an additional thermodynamic first-passage time parameter, nonequilibrium statistical operator method and extended irreversible thermodynamics with flows as an additional thermodynamic parameter. Thermodynamics containing an additional thermodynamic first-passage time parameter maps to extended irreversible thermodynamics. Various conditions for the dependence of the distribution parameters of the first-passage time on the random value of energy, the first thermodynamic parameter, are considered. Time parameter relaxation time τ of extended irreversible thermodynamics is replaced by the average first-passage time. Expressions are obtained for the thermodynamic parameter, the conjugate of the first passage time through the entropy change, and for the average first passage time through the flows.

cond-mat.stat-mech↗

arXiv2024

Probabilistic assessment of the reactor vessel lifetime

A simple and rapid method is proposed for assessing the reduction in the lifetime of steel walls of the reactor vessel under neutron irradiation. The method is based on modeling the number of radiation defects by the behavior of a general time-dependent random process of death and birth and queuing theory. Necessary data for assessments: the estimated operating time of the reactor (in years), the actual operating time of the reactor, the accumulated fluence depending on time, the temperature on the walls of the reactor vessel, the neutron absorption cross section of the steel of the reactor walls, the energy of fast neutrons striking the walls. The main problem: getting this accurate data.

physics.ins-det↗