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Fluctuation theorems are fundamental results in nonequilibrium thermodynamics beyond the linear response regime. Among these, the paradigmatic Tasaki-Crooks fluctuation theorem relates the statistics of the works done in a forward…

Statistical Mechanics · Physics 2024-06-19 Gianluca Francica , Luca Dell'Anna

The fluctuation theorem for entropy production is a remarkable symmetry of the distribution of produced entropy that holds universally in non-equilibrium steady states with Markovian dynamics. However, in systems with slow degrees of…

Statistical Mechanics · Physics 2018-02-21 Matthias Uhl , Patrick Pietzonka , Udo Seifert

Fluctuation theorems are a generalization of thermodynamics on small scales and provide the tools to characterize the fluctuations of thermodynamic quantities in non-equilibrium nanoscale systems. They are particularly important for…

Statistical Mechanics · Physics 2014-04-03 Jan Gieseler , Romain Quidant , Christoph Dellago , Lukas Novotny

We consider work fluctuation relations (FRs) for generic types of dynamics generating anomalous diffusion: Levy flights, long-correlated Gaussian processes and time-fractional kinetics. By combining Langevin and kinetic approaches we…

Statistical Mechanics · Physics 2009-03-24 A. V. Chechkin , R. Klages

We study the relation between the microscopic properties of a many-body system and the electron spectra, experimentally accessible by photoemission. In a recent paper [Phys. Rev. Lett. 114, 236402 (2015)], we introduced the "fluctuation…

Strongly Correlated Electrons · Physics 2018-03-28 O. Gunnarsson , J. Merino , T. Schäfer , G. Sangiovanni , G. Rohringer , A. Toschi

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum…

Statistical Mechanics · Physics 2026-01-12 Paul Menczel , Christian Flindt , Fredrik Brange , Franco Nori , Clemens Gneiting

A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…

Statistical Mechanics · Physics 2015-06-18 Matteo Colangeli , Lamberto Rondoni , Antonella Verderosa

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…

Statistical Mechanics · Physics 2025-04-09 Jonas H. Fritz , Benjamin Ertel , Udo Seifert

We present a new approach to fluctuation identities for reflected L\'{e}vy processes with one-sided jumps. This approach is based on a number of easy to understand observations and does not involve excursion theory or It\^{o} calculus. It…

Probability · Mathematics 2010-04-23 Jevgenijs Ivanovs

Numerical observations on a Markov chain and on the continuous Markov process performed by a granular tracer show that the ``usual'' fluctuation relation for a given observable is not verified for finite (but arbitrarily large) times. This…

Statistical Mechanics · Physics 2007-05-23 Andrea Puglisi , Lamberto Rondoni , Angelo Vulpiani

Linear diffusions are used to model a large number of stochastic processes in physics, including small mechanical and electrical systems perturbed by thermal noise, as well as Brownian particles controlled by electrical and optical forces.…

Statistical Mechanics · Physics 2023-05-10 Johan du Buisson , Hugo Touchette

In small systems where relevant energies are comparable to thermal agitation, fluctuations are of the order of average values. In systems in thermodynamical equilibrium, the variance of these fluctuations can be related to the dissipation…

Statistical Mechanics · Physics 2007-05-23 Nicolas Garnier , Ciliberto Sergio

We show how a general formulation of the Fluctuation-Response Relation is able to describe in detail the connection between response properties to external perturbations and spontaneous fluctuations in systems with fast and slow variables.…

Chaotic Dynamics · Physics 2020-01-29 Guglielmo Lacorata , Angelo Vulpiani

We derive a set of isometric fluctuation relations, which constrain the order parameter fluctuations in finite-size systems at equilibrium and in the presence of a broken symmetry. These relations are exact and should apply generally to…

Statistical Mechanics · Physics 2015-06-23 D. Lacoste , P. Gaspard

A Fluctuation Theorem (FT), both Classical and Quantum, describes the large-deviations in the approach to equilibrium of an isolated quasi-integrable system. Two characteristics make it unusual: (i) it concerns the internal dynamics of an…

Statistical Mechanics · Physics 2018-11-14 Tomer Goldfriend , Jorge Kurchan

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a…

Statistical Mechanics · Physics 2015-05-14 Jan Derezinski , Wojciech De Roeck , Christian Maes

We solve two problems related to the fluctuations of time-integrated functionals of Markov diffusions, used in physics to model nonequilibrium systems. In the first we derive and illustrate the appropriate boundary conditions on the…

Statistical Mechanics · Physics 2023-02-01 Johan du Buisson

Thermodynamics is usually formulated on the presumption that the observer has complete information about the system he/she deals with: no parasitic current, exact evaluation of the forces that drive the system. For example, the acclaimed…

Statistical Mechanics · Physics 2017-12-15 Matteo Polettini , Massimiliano Esposito

Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of…

Statistical Mechanics · Physics 2020-03-25 Jeremy A. Owen , Todd R. Gingrich , Jordan M. Horowitz

From the perspective of quantum thermodynamics, realisable measurements cost work and result in measurement devices that are not perfectly correlated with the measured systems. We investigate the consequences for the estimation of work in…

Quantum Physics · Physics 2019-11-05 Tiago Debarba , Gonzalo Manzano , Yelena Guryanova , Marcus Huber , Nicolai Friis
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