Related papers: Generalized black-box large deviation simulations:…
An introduction to numerical large-deviation sampling is provided. First, direct biasing with a known distribution is explained. As simple example, the Bernoulli experiment is used throughout the text. Next, Markov chain Monte Carlo (MCMC)…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
In this paper we develop the large deviations principle and a rigorous mathematical framework for asymptotically efficient importance sampling schemes for general, fully dependent systems of stochastic differential equations of slow and…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
According to the Jarzynski theorem, equilibrium free energy differences can be calculated from the statistics of work carried out during non-equilibrium transformations. Although exact, this approach can be plagued by large statistical…
This thesis is devoted to the theoretical study of slow thermodynamic processes in non-equilibrium stochastic systems. Its main result is a physically and mathematically consistent construction of relevant thermodynamic quantities in the…
We introduce a numerical procedure to evaluate directly the probabilities of large deviations of physical quantities, such as current or density, that are local in time. The large-deviation functions are given in terms of the typical…
We investigate the nucleation dynamics of the three-dimensional random field Ising model (RFIM) under an external field. We use umbrella sampling to compute the free-energy cost of a critical nucleus, and use forward flux sampling for the…
We calculate the probability distribution of work for an exactly solvable model of a system interacting with its environment. The system of interest is a harmonic oscillator with a time dependent control parameter, the environment is…
The equilibrium size distribution function of clusters (nanoparticles) in the system of finite number of molecules (atoms) in finite closed volume with constant total energy (isolated system) is found using methods of statistical…
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
A Hamiltonian-based model of many harmonically interacting massive particles that are subject to linear friction and coupled to heat baths at different temperatures is used to study the dynamic approach to equilibrium and non-equilibrium…
We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a…
A central endeavor of thermodynamics is the measurement of free energy changes. Regrettably, although we can measure the free energy of a system in thermodynamic equilibrium, typically all we can say about the free energy of a…
We obtain the large deviation function for entropy production of the medium and its distribution function for two-site totally asymmetric simple exclusion process(TASEP) and three-state unicyclic network. Since such systems are described…
We derive the optimal estimates of the free energies of an arbitrary number of thermodynamic states from nonequilibrium work measurements; the work data are collected from forward and reverse switching processes and obey a fluctuation…
Generative models have advanced significantly in sampling material systems with continuous variables, such as atomistic structures. However, their application to discrete variables, like atom types or spin states, remains underexplored. In…
Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…