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We develop a theory for inferring equilibrium transition rates from trajectories driven by a time dependent force using results from stochastic thermodynamics. Applying the Kawasaki relation to approximate the nonequilibrium distribution…

Chemical Physics · Physics 2023-05-17 Benjamin Kuznets-Speck , David T Limmer

We establish a connection between stochastic optimal control and generative models based on stochastic differential equations (SDEs), such as recently developed diffusion probabilistic models. In particular, we derive a…

Machine Learning · Computer Science 2024-03-27 Julius Berner , Lorenz Richter , Karen Ullrich

We consider optimization of the average entropy production in inhomogeneous temperature environments within the framework of stochastic thermodynamics. For systems modeled by Langevin equations (e.g. a colloidal particle in a heat bath) it…

Statistical Mechanics · Physics 2013-03-14 Stefano Bo , Erik Aurell , Ralf Eichhorn , Antonio Celani

A fundamental result of thermodynamic geometry is that the optimal, minimal-work protocol that drives a nonequilibrium system between two thermodynamic states in the slow-driving limit is given by a geodesic of the friction tensor, a…

Statistical Mechanics · Physics 2024-10-24 Adrianne Zhong , Michael R. DeWeese

What are the fundamental limitations placed by the laws of thermodynamics on the energy expenditure needed to carry out a given task in a nonequilibrium environment in finite time? In this thesis, we investigate "optimal nonequilibrium…

Statistical Mechanics · Physics 2025-09-30 Adrianne Zhong

Statistical divergences are important tools in data analysis, information theory, and statistical physics, and there exist well known inequalities on their bounds. However, in many circumstances involving temporal evolution, one needs…

Data Analysis, Statistics and Probability · Physics 2025-03-25 Jan Karbowski

In this paper we study model reduction of linear and bilinear quadratic stochastic control problems with parameter uncertainties. Specifically, we consider slow-fast systems with unknown diffusion coefficient and study the convergence of…

Optimization and Control · Mathematics 2021-02-10 Hafida Bouanani , Carsten Hartmann , Omar Kebiri

In this work, we present a theoretical and computational framework for constructing stochastic transport maps between probability distributions using diffusion processes. We begin by proving that the time-marginal distribution of the sum of…

Probability · Mathematics 2025-03-27 Xicheng Zhang

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

Statistical Mechanics · Physics 2024-06-24 Jérémie Klinger , Grant M. Rotskoff

Seifert derived an exact fluctuation relation for diffusion processes using the concept of "stochastic system entropy". In this note we extend his formalism to entropic transport. We introduce the notion of relative stochastic entropy, or…

Statistical Mechanics · Physics 2012-11-30 Matteo Smerlak

This paper investigates the optimal control problem for a class of parabolic equations where the diffusion coefficient is influenced by a control function acting nonlocally. Specifically, we consider the optimization of a cost functional…

Optimization and Control · Mathematics 2025-03-11 Stefana-Lucia Anita , Luca Di Persio

Part I of this work [2] developed the exact diffusion algorithm to remove the bias that is characteristic of distributed solutions for deterministic optimization problems. The algorithm was shown to be applicable to a larger set of…

Optimization and Control · Mathematics 2017-12-27 Kun Yuan , Bicheng Ying , Xiaochuan Zhao , Ali H. Sayed

Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the…

Machine Learning · Statistics 2024-03-08 Gen Li , Yuting Wei , Yuxin Chen , Yuejie Chi

Near equilibrium, thermodynamic intuition suggests that fast, irreversible processes will dissipate more energy and entropy than slow, quasistatic processes connecting the same initial and final states. Here, we test the hypothesis that…

Statistical Mechanics · Physics 2022-12-07 Rebecca A. Bone , Daniel J. Sharpe , David J. Wales , Jason R. Green

We obtain equilibration rates for a one-dimensional nonlocal Fokker-Planck equation with time-dependent diffusion coefficient and drift, modeling the relaxation of a large swarm of robots, feeling each other in terms of their distance,…

Analysis of PDEs · Mathematics 2023-06-06 Ferdinando Auricchio , Giuseppe Toscani , Mattia Zanella

The question of deriving general force/flux relationships that apply out of the linear response regime is a central topic of theories for nonequilibrium statistical mechanics. This work applies an information theory perspective to compute…

Statistical Mechanics · Physics 2019-02-04 David M. Rogers

We study the contribution of advection by thermal velocity fluctuations to the effective diffusion coefficient in a mixture of two identical fluids. The steady-state diffusive flux in a finite system subject to a concentration gradient is…

Mesoscale and Nanoscale Physics · Physics 2015-05-27 A. Donev , A. de la Fuente , J. B. Bell , A. L. Garcia

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…

Optimization and Control · Mathematics 2023-08-22 Shuzhen Yang

Diffusion models have revolutionized various application domains, including computer vision and audio generation. Despite the state-of-the-art performance, diffusion models are known for their slow sample generation due to the extensive…

Machine Learning · Computer Science 2024-06-25 Zehao Dou , Minshuo Chen , Mengdi Wang , Zhuoran Yang

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…

Numerical Analysis · Mathematics 2022-05-25 Liu Liu , Lorenzo Pareschi , Xueyu Zhu