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We study fluctuations of the empirical processes of a non-equilibrium interacting particle system consisting of two species over a domain that is recently introduced in [8] and establish its functional central limit theorem. This…

Probability · Mathematics 2021-01-12 Zhen-Qing Chen , Wai-Tong Louis Fan

We study single-variable approaches for describing stochastic dynamics with small inertia. The basic models we deal with describe passive Brownian particles and phase elements (phase oscillators, rotators, superconducting Josephson…

Statistical Mechanics · Physics 2025-12-23 Denis S. Goldobin , Lyudmila S. Klimenko , Irina V. Tyulkina , Vasily A. Kostin , Lev A. Smirnov

Fractional Brownian motion is a non-Markovian Gaussian process indexed by the Hurst exponent $H\in [0,1]$, generalising standard Brownian motion to account for anomalous diffusion. Functionals of this process are important for practical…

Statistical Mechanics · Physics 2021-11-24 Tridib Sadhu , Kay Jörg Wiese

We briefly review the problem of Brownian motion and describe some intriguing facets. The problem is first treated in its original form as enunciated by Einstein, Langevin, and others. Then, utilizing the problem of Brownian motion as a…

Statistical Mechanics · Physics 2026-02-17 Sushanta Dattagupta , Aritra Ghosh

The large deviations analysis of solutions to stochastic differential equations and related processes is often based on approximation. The construction and justification of the approximations can be onerous, especially in the case where the…

Probability · Mathematics 2008-08-28 Amarjit Budhiraja , Paul Dupuis , Vasileios Maroulas

We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked to the theory of phase transitions. We also provide examples of new kinds of transient behaviour.

Dynamical Systems · Mathematics 2013-09-12 Godofredo Iommi , Mike Todd

Quantum phase transitions are a cornerstone of many-body physics at low temperatures but have remained elusive far from equilibrium. Driven open quantum systems -- a prominent non-equilibrium platform where coherent dynamics competes with…

Quantum Gases · Physics 2025-05-30 Naushad A. Kamar , Mostafa Ali , Mohammad Maghrebi

Brownian circuits perform computations using stochastic transitions driven by thermal fluctuations. While the energetic costs of such fluctuation-driven computation have been extensively studied within stochastic thermodynamics, much less…

Statistical Mechanics · Physics 2026-02-19 Kota Okajima , Koji Hukushima

Consider ``stochastic differential equations" driven by fractional Brownian motion with Hurst parameter H (1/4 <H< 1). Their solutions are sometimes called fractional diffusion processes. The main purpose of this paper is conditioning these…

Probability · Mathematics 2025-12-02 Yuzuru Inahama

We study the fluctuation properties of the local time density, ${\rho _T} = \frac{1}{T}\int_0^T {\delta ( {r(t) - 1} )} dt$, spent by a $d$-dimensional Brownian particle at a spherical shell of unit radius, where $r(t)$ denotes the radial…

Statistical Mechanics · Physics 2025-11-17 Ruofei Yan , Hanshuang Chen

We introduce a class of Markov coalescent processes on the continuous $d$-dimensional torus, in the most general setting of simultaneous multiple mergers, called the Brownian spatial coalescent. It is axiomatically defined through a…

Probability · Mathematics 2026-03-17 Peter Koepernik

Dynamical scaling is an asymptotic property typical for the dynamics of first-order phase transitions in physical systems and related to self-similarity. Based on the integral-representation for the marginal probabilities of a fractional…

Probability · Mathematics 2021-07-23 Markus Kreer

Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at Level 2.5 for the joint probability of…

Statistical Mechanics · Physics 2021-05-07 Cecile Monthus

Large dynamical fluctuations - atypical realizations of the dynamics sustained over long periods of time - can play a fundamental role in determining the properties of collective behavior of both classical and quantum non-equilibrium…

Statistical Mechanics · Physics 2018-07-18 Federico Carollo , Juan P. Garrahan , Igor Lesanovsky , Carlos Pérez-Espigares

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

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…

Statistical Mechanics · Physics 2011-11-29 Vivien Lecomte , Cécile Appert-Rolland , Frédéric van Wijland

We consider a model of active Brownian particles with velocity-alignment in two spatial dimensions with passive and active fluctuations. Hereby, active fluctuations refers to purely non-equilibrium stochastic forces correlated with the…

Statistical Mechanics · Physics 2016-05-02 Robert Grossmann , Lutz Schimansky-Geier , Pawel Romanczuk

In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…

Statistical Mechanics · Physics 2017-09-19 A. Faggionato

We consider the problem of conditioning a Markov process on a rare event and of representing this conditioned process by a conditioning-free process, called the effective or driven process. The basic assumption is that the rare event used…

Statistical Mechanics · Physics 2015-08-17 Raphael Chetrite , Hugo Touchette

We investigate collective behavior of a system of two-dimensional interacting Brownian particles in the hydrodynamic regime. By means of the Martin-Siggia-Rose-Jenssen-de Dominicis formalism, we built up a generating functional for…

Statistical Mechanics · Physics 2025-03-10 Nathan O Silvano , Daniel G. Barci