Related papers: Improved linear response for stochastically driven…
Stationary non-equilibrium states describe steady flows through macroscopic systems. Although they represent the simplest generalization of equilibrium states, they exhibit a variety of new phenomena. Within a statistical mechanics…
A reduced chemical scheme involving a small number of variables is often sufficient to account for the deterministic evolution of the concentrations of the main species contributing to a reaction. However its predictions are questionable in…
Starting at the mesoscopic level with a general formulation of stochastic thermodynamics in terms of Markov jump processes, we identify the scaling conditions that ensure the emergence of a (typically nonlinear) deterministic dynamics and…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Deducing the states of spatiotemporally chaotic systems (SCSs) as they evolve in time is crucial for various applications. However, it is a dramatic challenge for generally achieving so due to the complexity of non-periodic dynamics and the…
With the rapid increase of valuable observational, experimental and simulating data for complex systems, great efforts are being devoted to discovering governing laws underlying the evolution of these systems. However, the existing…
We consider a quantum system driven out of equilibrium via a small Hamiltonian perturbation. Building on the paradigmatic framework of linear response theory (LRT), we derive an expression for the full generating function of the dissipated…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Non-Markovian stochastic Langevin-like equations of motion are compared to their corresponding Markovian (local) approximations. The validity of the local approximation for these equations, when contrasted with the fully nonlocal ones, is…
We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification…
We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…
Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining…
We consider the problem to steer a linear dynamical system with full state observation from an initial gaussian distribution in state-space to a final one with minimum energy control. The system is stochastically driven through the control…
This work studies the design problem of feedback stabilizers for discrete-time systems with input delays. A backstepping procedure is proposed for disturbance-free discrete-time systems. The feedback law designed by using backstepping…
The influence of dissipation on the fluctuation statistics of the total energy is investigated through both a phenomenological and a stochastic model for dissipative energy-transfer through a cascade of states. In equilibrium the states…
In this study, we develop a stochastic optimal control approach with reinforcement learning structure to learn the unknown parameters appeared in the drift and diffusion terms of the stochastic differential equation. By choosing an…
The forecasting and computation of the stability of chaotic systems from partial observations are tasks for which traditional equation-based methods may not be suitable. In this computational paper, we propose data-driven methods to (i)…
We consider the task of generating discrete-time realisations of a nonlinear multivariate diffusion process satisfying an It\^o stochastic differential equation conditional on an observation taken at a fixed future time-point. Such…
We derive various exact results for Markovian systems that spontaneously relax to a non-equilibrium steady-state by using joint probability distributions symmetries of different entropy production decompositions. The analytical approach is…