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We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…

Dynamical Systems · Mathematics 2017-09-05 Luke Mohr , Hong-Kun Zhang

Irreversible drift-diffusion processes are very common in biochemical reactions. They have a non-equilibrium stationary state (invariant measure) which does not satisfy detailed balance. For the corresponding Fokker-Planck equation on a…

Numerical Analysis · Mathematics 2023-04-12 Yuan Gao , Jian-Guo Liu

The large-time asymptotics of weak solutions to Maxwell--Stefan diffusion systems for chemically reacting fluids with different molar masses and reversible reactions are investigated. The diffusion matrix of the system is generally neither…

Analysis of PDEs · Mathematics 2019-07-29 Esther S. Daus , Ansgar Jüngel , Bao Quoc Tang

We present a novel simulation-free framework for training continuous-time diffusion processes over very general objective functions. Existing methods typically involve either prescribing the optimal diffusion process -- which only works for…

Machine Learning · Computer Science 2025-06-24 Mengjian Hua , Eric Vanden-Eijnden , Ricky T. Q. Chen

We attempt to characterize irreversibility of a dynamical system from the existence of different forward and backward mathematical representations depending on the direction of the time arrow. Such different representations have been…

Dynamical Systems · Mathematics 2025-08-13 Giorgio Picci

The unified description of diffusion processes that cross over from a ballistic behavior at short times to normal or anomalous diffusion (sub- or superdiffusion) at longer times is constructed on the basis of a non-Markovian generalization…

Statistical Mechanics · Physics 2013-03-26 Valery Ilyin , Itamar Procaccia , Anatoly Zagorodny

This paper revisits the modeling of multicomponent diffusion within the framework of thermodynamics of irreversible processes. We briefly review the two well-known main approaches, leading to the generalized Fick-Onsager multicomponent…

Mathematical Physics · Physics 2020-08-13 Dieter Bothe , Pierre-Etienne Druet

In genuine nonequilibrium systems that undergo continuous driving, the thermodynamic forces are nonconservative, meaning they cannot be described by any free energy potential. Nonetheless, we show that the dynamics of such systems are…

Statistical Mechanics · Physics 2026-04-10 Artemy Kolchinsky , Andreas Dechant , Kohei Yoshimura , Sosuke Ito

Computing the stochastic entropy production associated with the evolution of a stochastic dynamical system is a well-established problem. In a small number of cases such as the Ornstein-Uhlenbeck process, of which we give a complete…

Statistical Mechanics · Physics 2020-08-26 Richard J Martin , Ian J Ford

We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand…

Soft Condensed Matter · Physics 2016-05-25 Daniel de las Heras , Joseph M. Brader , Andrea Fortini , Matthias Schmidt

The entropy production rate is a central quantity in non-equilibrium statistical physics, scoring how far a stochastic process is from being time-reversible. In this paper, we compute the entropy production of diffusion processes at…

Statistical Mechanics · Physics 2023-06-19 Lancelot Da Costa , Grigorios A. Pavliotis

This work extends the results of the recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We aim at investigating the question that…

Statistical Mechanics · Physics 2011-05-30 Moises Santillan , Hong Qian

This work is concerned with model reduction of stochastic differential equations and builds on the idea of replacing drift and noise coefficients of preselected relevant, e.g. slow variables by their conditional expectations. We extend…

Analysis of PDEs · Mathematics 2020-03-05 Carsten Hartmann , Lara Neureither , Upanshu Sharma

The stochastic theory of non-relativistic quantum mechanics presented here relies heavily upon the theory of stochastic processes, with its definitions, theorems and specific vocabulary as well. Its main hypothesis states indeed that the…

Quantum Physics · Physics 2014-04-01 Maurice J. M. L. O. Godart

The global-in-time existence of bounded weak solutions to the Maxwell-Stefan-Fourier equations in Fick-Onsager form is proved. The model consists of the mass balance equations for the partial mass densities and and the energy balance…

Analysis of PDEs · Mathematics 2020-11-02 Christoph Helmer , Ansgar Jüngel

General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…

Astrophysics of Galaxies · Physics 2017-06-20 Jean Heyvaerts , Jean-Baptiste Fouvry , Pierre-Henri Chavanis , Christophe Pichon

Entropy, its production, and its change in a dynamical system can be understood from either a fully stochastic dynamic description or from a deterministic dynamics exhibiting chaotic behavior. By taking the former approach based on the…

Mathematical Physics · Physics 2025-08-26 Hong Qian , Zhongwei Shen

We carry out a comprehensive linear stability analysis of active Brownian particle systems around a constant homogeneous state. These scalar models, being important prototypes for the continuous description of active matter, are…

Analysis of PDEs · Mathematics 2025-12-22 Michele Coti Zelati , Lucas Ertzbischoff , David Gerard-Varet

We explore the effect of stochastic resetting on the first-passage properties of space-dependent diffusion in presence of a constant bias. In our analytically tractable model system, a particle diffusing in a linear potential…

Statistical Mechanics · Physics 2020-12-23 Somrita Ray

Detailed fluctuation theorem, a microscopic version of the steady state fluctuation theorem, has been proposed by Jarzynski and demonstrated in the case of Hamiltonian systems weakly coupled with reservoirs. We show that an identical…

Statistical Mechanics · Physics 2010-07-20 K. Gururaj , G. Raghavan , M. C. Valsakumar