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We review an scenario for the non-equilibrium dynamics of glassy systems that has been motivated by the exact solution of simple models. This approach allows one to set on firmer grounds well-known phenomenological theories. The old ideas…

Statistical Mechanics · Physics 2009-11-07 Leticia F. Cugliandolo

We study the dynamical behaviour of mesoscopic systems in contact with a thermal bath, described either via a non-linear Langevin equation at the trajectory level -- or the corresponding Fokker-Planck equation for the probability…

Statistical Mechanics · Physics 2024-03-26 A. Patrón , B. Sánchez-Rey , E. Trizac , A. Prados

By using the effective non-Markovian measure [H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009)], we investigate non-Markovian dynamics of a pair of two-level atoms (TLAs) system, each of which interacting with a local…

Quantum Physics · Physics 2017-02-16 Li Jiang , Guo-Feng Zhang

The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…

Statistical Mechanics · Physics 2017-01-05 Thomas Speck

A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It…

Statistical Mechanics · Physics 2015-10-28 Chulan Kwon

This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…

Statistical Mechanics · Physics 2015-12-18 L. Bertini , A. De Sole , D. Gabrielli , G. Jona--Lasinio , C. Landim

According to Harada and Sasa [Phys. Rev. Lett. 95, 130602 (2005)], heat production generated in a non-equilibrium steady state can be inferred from measuring response and correlation functions. In many colloidal systems, however, it is a…

Soft Condensed Matter · Physics 2015-06-11 Boris Lander , Jakob Mehl , Valentin Blickle , Clemens Bechinger , Udo Seifert

We consider a situation where an $N$-level system (NLS) is coupled to a heat bath without being necessarily thermalized. For this situation we derive general Jarzinski-type equations and conclude that heat and entropy is flowing from the…

Quantum Physics · Physics 2021-08-25 Heinz-Jürgen Schmidt , Jürgen Schnack , Jochen Gemmer

We extend the canonical Gibbs distribution, originally formulated for systems at equilibrium, to systems driven out of equilibrium. The stochastic dynamics of a small system are described by a probability distribution over discrete energy…

Statistical Mechanics · Physics 2026-03-31 Jean-Luc Garden

The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which…

Statistical Mechanics · Physics 2023-09-13 Davide Venturelli , Andrea Gambassi

Most natural thermodynamic systems operate far from equilibrium, developing persistent currents and organizing into non-equilibrium stationary states (NESSs). Yet, the principles by which such systems self-organize, breaking equilibrium…

Statistical Mechanics · Physics 2025-11-11 Matteo Sireci , Luca Peliti , Daniel Maria Busiello

We present a method of estimating the rate of entropy production in underdamped dynamics by decomposing it into contributions originating in different non-equilibrium effects. Specifically, a non-zero average velocity, a non-thermal width…

Statistical Mechanics · Physics 2025-12-01 Mario A. Ciampini , Jakob Rieser , Nikolai Kiesel , Andreas Dechant

Inspired by one--dimensional light--particle systems, the dynamics of a non-Hamiltonian system with long--range forces is investigated. While the molecular dynamics does not reach an equilibrium state, it may be approximated in the…

Statistical Mechanics · Physics 2019-01-23 Romain Bachelard , Nicola Piovella , Shamik Gupta

Biologically driven non-equilibrium fluctuations are often characterized by their non-Gaussianity or by an "effective temperature", which is frequency dependent and higher than the ambient temperature. We address these two measures…

Biological Physics · Physics 2011-06-16 Eyal Ben-Isaac , YongKeun Park , Gabriel Popescu , Frank L. H. Brown , Nir S. Gov , Yair Shokef

Dissipative particle dynamics (DPD) does not conserve energy and this precludes its use in the study of thermal processes in complex fluids. We present here a generalization of DPD that incorporates an internal energy and a temperature…

Statistical Mechanics · Physics 2016-08-15 Pep Español

High-intensity THz laser pulses enable the light-mediated control of lattice vibrations by resonantly driving selected phonon modes. On ultrafast timescales, memory effects influence the phonon dynamics and must be accounted for to describe…

Materials Science · Physics 2026-03-10 Fredrik Erikssonm Yulong Qiao , Erik Fransson , R. Matthias Geilhufe , Paul Erhart

We address the challenge of incorporating non-Markovian electronic friction effects in quantum-mechanical approximations of dynamical observables. A generalized Langevin equation (GLE) is formulated for ring-polymer molecular dynamics…

Materials Science · Physics 2025-06-04 George Trenins , Mariana Rossi

A diffusion process of a Brownian particle in a medium of temperature $T$ is re-considered. We assume that temperature of the medium fluctuates around its mean value. The velocity probability distribution is obtained. It is shown that the…

Statistical Mechanics · Physics 2007-05-23 J. Luczka , B. Zaborek

In these lecture notes, the basic principles of stochastic thermodynamics are developed starting with a closed system in contact with a heat bath. A trajectory undergoes Markovian transitions between observable meso-states that correspond…

Statistical Mechanics · Physics 2018-06-13 Udo Seifert

The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…

Quantum Physics · Physics 2009-11-13 Denis Lacroix
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