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The analysis of fluctuation-dissipation relations developed in Giona et al. (2024) for particle hydromechanics is extended to stochastic forcings alternative to Wiener processes, with the aim of addressing the occurrence of Gaussian…

Statistical Mechanics · Physics 2024-12-30 Chiara Pezzotti , Massimiliano Giona , Giuseppe Procopio

Anomalous diffusion is an established phenomenon but still a theoretical challenge in non-equilibrium statistical mechanics. Physical models are built incrementally, and the most recent and most general family is based on the fractional…

Probability · Mathematics 2025-07-23 Christian Bender , Yana A. Butko , Mirko D'Ovidio , Gianni Pagnini

We review generalized Fluctuation-Dissipation Relations which are valid under general conditions even in ``non-standard systems'', e.g. out of equilibrium and/or without a Hamiltonian structure. The response functions can be expressed in…

Statistical Mechanics · Physics 2019-09-10 A. Sarracino , A. Vulpiani

Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian…

Statistical Mechanics · Physics 2021-03-24 A. Chechkin , I. M. Sokolov

Brownian particles in random potentials show an extended regime of subdiffusive dynamics at intermediate times. The asymptotic diffusive behavior is often established at very long times and thus cannot be accessed in experiments or…

Soft Condensed Matter · Physics 2014-05-22 Richard D. L. Hanes , Michael Schmiedeberg , Stefan U. Egelhaaf

Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous…

Statistical Mechanics · Physics 2022-01-19 Xudong Wang , Yao Chen

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise,…

Machine Learning · Statistics 2026-05-20 Wenpin Tang , Nizar Touzi , Zikun Zhang , Xun Yu Zhou

In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…

Statistical Mechanics · Physics 2023-08-01 Adrian Pacheco-Pozo , Igor M. Sokolov

A rapidly increasing number of systems is identified in which the stochastic motion of tracer particles follows the Brownian law $\langle\mathbf{r}^2(t) \rangle\simeq Dt$ yet the distribution of particle displacements is strongly…

Statistical Mechanics · Physics 2019-01-30 V. Sposini , A. V. Chechkin , R. Metzler

Einstein's explanation of Brownian motion provided one of the cornerstones which underlie the modern approaches to stochastic processes. His approach is based on a random walk picture and is valid for Markovian processes lacking long-term…

Statistical Mechanics · Physics 2009-11-10 I. M. Sokolov , J. Klafter

The dynamics of a one-dimensional stochastic model is studied in presence of an absorbing boundary. The distribution of fluctuations is analytically characterized within the generalized van Kampen expansion, accounting for higher order…

Statistical Mechanics · Physics 2015-05-28 Claudia Cianci , Francesca Di Patti , Duccio Fanelli

We present a model of anomalous diffusion consisting of an ensemble of particles undergoing homogeneous Brownian motion except for confinement by randomly placed reflecting boundaries. For power-law distributed compartment sizes, we…

Soft Condensed Matter · Physics 2015-06-09 Gerald John Lapeyre

We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…

Probability · Mathematics 2018-11-07 Sebastian Andres , Lisa Hartung

We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear…

Statistical Mechanics · Physics 2026-03-12 Marco Bussoletti , Mirko Gallo , Amir Jafari , Gregory L. Eyink

We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…

Statistical Mechanics · Physics 2007-05-23 M. Annunziato , P. Grigolini , J. Riccardi

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

.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…

Statistical Mechanics · Physics 2020-08-26 V. Sposini , D. S. Grebenkov , R. Metzler , G. Oshanin , F. Seno

We focus on the dynamics of a Brownian particle whose mass fluctuates. First we show that the behaviour is similar to that of a Brownian particle moving in a fluctuating medium, as studied by Beck [Phys. Rev. Lett. 87 (2001) 180601]. By…

Statistical Mechanics · Physics 2007-06-13 R. Lambiotte , M. Ausloos

Fickian yet non-Gaussian diffusion is a ubiquitous phenomenon observed in various biological and soft matter systems. This anomalous dynamics is typically attributed to heterogeneous environments inducing spatiotemporal variations in the…

Statistical Mechanics · Physics 2025-03-20 Seongyu Park , Xavier Durang , Ralf Metzler , Jae-Hyung Jeon

In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with…

Statistical Mechanics · Physics 2024-06-13 Go Uchida , Hitoshi Washizu , Hiromi Miyoshi