Related papers: Langevin dynamics neglecting detailed balance cond…
It is known that the distribution of nonreversible Markov processes breaking the detailed balance condition converges faster to the stationary distribution compared to reversible processes having the same stationary distribution. This is…
For the description of thermally activated dynamics in systems of classical magnetic moments numerical methods are desirable. We consider a simple model for isolated magnetic particles in a uniform field with an oblique angle to the easy…
We study the Langevin dynamics of a physical system with manifold structure $\mathcal{M}\subset\mathbb{R}^p$ based on collected sample points $\{\mathsf{x}_i\}_{i=1}^n \subset \mathcal{M}$ that probe the unknown manifold $\mathcal{M}$.…
In this paper, we develop a theoretical framework for nonlinear stochastic optimal control problems with optimal stopping by establishing a density-based deterministic representation of the underlying diffusion. For state-independent…
We consider a classical model of non-equilibrium statistical mechanics accounting for non-Markovian effects, which is referred to as the Generalized Langevin Equation in the literature. We derive reduced Markovian descriptions obtained…
We study zero-sum games in the space of probability distributions over the Euclidean space $\mathbb{R}^d$ with entropy regularization, in the setting when the interaction function between the players is smooth and strongly convex-strongly…
We study the solution of the two-temperatures Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of…
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…
When simulating molecular systems using deterministic equations of motion (e.g., Newtonian dynamics), such equations are generally numerically integrated according to a well-developed set of algorithms that share commonly agreed-upon…
Recently it has been questioned, notably in the context of the scalar singlet dark matter model with $m_\varphi^{ }\simeq 60$ GeV, how efficiently kinetic equilibrium is maintained if freeze-out dynamics is pushed down to low temperatures…
Bridging the gap between individual agent behavior and macroscopic societal patterns is a central challenge in the social sciences. In this work, we propose a solution to this problem via a kinetic theory formulation. We demonstrate that…
Recently there has been remarkable progress in the complex Langevin method, which aims at solving the complex action problem by complexifying the dynamical variables in the original path integral. In particular, a new technique called the…
We address the problem of constructing accurate mathematical models of the dynamics of complex systems projected on a collective variable. To this aim we introduce a conceptually simple yet effective algorithm for estimating the parameters…
The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of…
A theoretical framework is developed for the phenomenon of non-Gaussian normal diffusion that has experimentally been observed in several heterogeneous systems. From the Fokker-Planck equation with the dynamical structure with largely…
In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality observing the…
Presentation of the probability as an intrinsic property of the nature leads researchers to switch from deterministic to stochastic description of the phenomena. The procedure of stochastization of one-step process was formulated. It allows…
Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…
Complex Langevin dynamics can be used to perform numerical simulations of theories with a complex action. In order to justify the procedure, it is important to understand the properties of the real and positive distribution, which is…
Statistical invariance of Wiener increments under SO(n) rotations provides a notion of gauge transformation of state-dependent Brownian motion. We show that the stochastic dynamics of non gauge-invariant systems is not unambiguously…