Fluctuation-dissipation: Response theory in statistical physics

By Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, Angelo Vulpiani. 2008

712 citations recorded by the source corpus.

Abstract General aspects of the Fluctuation–Dissipation Relation (FDR), and Response Theory are considered. After analyzing the conceptual and historical relevance of fluctuations in statistical mechanics, we illustrate the relation between the relaxation of spontaneous fluctuations, and the response to an external perturbation. These studies date back to Einstein’s work on Brownian Motion, were continued by Nyquist and Onsager and culminated in Kubo’s linear response theory. The FDR has been originally developed in the framework of statistical mechanics of Hamiltonian systems, nevertheless a generalized FDR holds under rather general hypotheses, regardless of the Hamiltonian, or equilibrium nature of the system. In the last decade, this subject was revived by the works on Fluctuation Relations (FR) concerning far from equilibrium systems. The connection of these works with large deviation theory is analyzed. Some examples, beyond the standard applications of statistical mechanics, where fluctuations play a major role are discussed: fluids, granular media, nanosystems and biological systems.

Subfields: Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/88cea854916b7068dfdd0308d4930c96a5c74454

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Citations in the corpus

Non-equilibrium statistical mechanics: from a paradigmatic model to biological transport (2011, neutral): “2429 [80] Marconi UMB, Puglisi A, Rondoni L, Vulpiani A.”
Climate Sensitivity via a Nonparametric Fluctuation–Dissipation Theorem (2011, background): “df(t t) dt, (1) where superscript T denotes the matrix transpose (Deker and Haake 1975; Hänggi and Thomas 1977; Risken 1984; Majda et al. 2005; Marconi et al. 2008).”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “(Cugliandolo et al., 1997), e.g., for glassy systems (Bellon and Ciliberto, 2002; Crisanti and Ritort, 2003; Leuzzi, 2009) and models of driven matter (Berthier et al., 2000; Loi et al., 2008) (see also the review (Marconi et al., 2008)).”
Challenges in Climate Science and Contemporary Applied Mathematics (2012, background): “The fluctuation-dissipation theorem is one of the cornerstones of the statistical physics of identical molecules of gases and liquids [109].”
Mathematical and physical ideas for climate science (2013, background): “…one expects to see little influence of the fine structure of the invariant measure of chaotic deterministic systems, as projections from high-dimensional spaces to lower dimensional ones are involved(Marconi et al., 2008) and coarse-graining effects can be invoked (Wouters and Lucarini , 2013).”
The large deviation approach to statistical mechanics (2008, background): “To make sure that extended fluctuation theorems are not confused with the fluctuations theorems defined at the start of this section, it is common to refer to the latter ones as conventional fluctuation theorems [171,205,206].”
Irreversibility in Active Matter Systems: Fluctuation Theorem and Mutual Information (2018, background): “[60] Umberto Marini Bettolo Marconi, Andrea Puglisi, Lamberto Rondoni, and Angelo Vulpiani, “Fluctuation– dissipation: response theory in statistical physics,” Physics reports 461, 111–195 (2008).”
Stochastic thermodynamics, fluctuation theorems and molecular machines (2012, background): “A comprehensive review of the general relation between fluctuations and response including, in particular, deterministic chaotic systems is given in [316].”
Temperature in and out of equilibrium: A review of concepts, tools and attempts (2017, background): “In the first half of the 20th century a series of important results, with different physical systems and observables, showed that many other similar relations exist, tying in the same way those three ingredients: spontaneous fluctuations, response and temperature [97, 14].”
The physics of climate variability and climate change (2019, background): “n internal, random uctuation. The FDT thus relates natural and forced uctuations of a system (e,g., Kubo, 1957, 1966); it is a cornerstone of statistical mechanics and has applications in many areas (Marconi et al., 2008, and references therein). We have emphasized already in Sect. III.B that, even ”