Fluctuation-dissipation: Response theory in statistical physics

  title={Fluctuation-dissipation: Response theory in statistical physics},
  author={Umberto Marini Bettolo Marconi and Andrea Puglisi and Lamberto Rondoni and Angelo Vulpiani},
  journal={Physics Reports},
Fluctuations, Linear Response, and Currents in Out-of-Equilibrium Systems
In this review we discuss, from an experimental point of view, several concepts of statistical mechanics for systems that are out of equilibrium either because they are driven by external forces or
Fluctuation–dissipation relations far from equilibrium: a case study
Motivated by the Mori–Zwanzig formalism, it is suggested to impose an orthogonality constraint on the stochastic force, which is in fact equivalent to the validity of this Volterra equation.
Fluctuation-dissipation relations far from equilibrium
The fluctuation-dissipation (F-D) theorem is a fundamental result for systems near thermodynamic equilibrium, and justifies studies between microscopic and macroscopic properties. It states that the
Beyond the linear fluctuation-dissipation theorem: the role of causality
In this paper we tackle the traditional problem of relating the fluctuations of a system to its response to external forcings and extend the classical theory in order to be able to encompass also
Fluctuation Relations and Nonequilibrium Response for Chaotic Dissipative Dynamics
In a recent paper [Colangeli and Rondoni, Physica D 241:681, 2011] it was argued that the Fluctuation Relation for the phase space contraction rate Λ could suitably be extended to non-reversible
Fluctuation-Dissipation and Fluctuation Relations: From Equilibrium to Nonequilibrium and Back
The fluctuation-dissipation relation is a most remarkable classical result of statistical physics, which allows us to understand nonequilibrium properties of thermodynamic systems from observations
The fluctuation-dissipation relation: how does one compare correlation functions and responses?
We discuss the well known Einstein and the Kubo fluctuation-dissipation relations (FDRs) in the wider framework of a generalized FDR for systems with a stationary probability distribution. A
An Investigation Into the Significance of Dissipation in Statistical Mechanics
The dissipation function is a key quantity in nonequilibrium statistical mechanics. It was originally derived for use in the Evans-Searles Fluctuation Theorem, which quantitatively describes thermal
Handy fluctuation-dissipation relation to approach generic noisy systems and chaotic dynamics.
A general formulation of the fluctuation-dissipation relations (FDRs) holding also in far-from-equilibrium stochastic dynamics, and allows to reproduce, in a suitable small-noise limit, the response functions of deterministic, strongly nonlinear dynamical models, even in the presence of chaotic behavior.
Fluctuation–dissipation relations in the absence of detailed balance: formalism and applications to active matter
We present a comprehensive study about the relationship between the way detailed balance is broken in non-equilibrium systems and the resulting violations of the fluctuation–dissipation theorem.


The fluctuation-dissipation theorem
The linear response theory has given a general proof of the fluctuation-dissipation theorem which states that the linear response of a given system to an external perturbation is expressed in terms
Fluctuation-dissipation relations in driven granular gases.
Two independent numerical experiments confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.
Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics
This paper reviews various applications of the theory of smooth dynamical systems to conceptual problems of nonequilibrium statistical mecanics. We adopt a new point of view which has emerged
Fully developed turbulence and statistical mechanics
This paper gives a self contained review of some recent progress of the statistical theory of fully developed turbulence. The emphasis is on both analogies and differences with Hamiltonian
The Fluctuation Theorem
The question of how reversible microscopic equations of motion can lead to irreversible macroscopic behaviour has been one of the central issues in statistical mechanics for more than a century. The
Power injected in dissipative systems and the fluctuation theorem
Abstract:We consider three examples of dissipative dynamical systems involving many degrees of freedom, driven far from equilibrium by a constant or time dependent forcing. We study the statistical
Fluctuation Relation beyond Linear Response Theory
The Fluctuation Relation (FR) is an asymptotic result on the distribution of certain observables averaged over time intervals T as T goes to infinity and it is a generalization of the
Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States
We formulate a dynamical fluctuation theory for stationary non-equilibrium states (SNS) which is tested explicitly in stochastic models of interacting particles. In our theory a crucial role is
Heat and fluctuations from order to chaos
Abstract.The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e. existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic