2008/03/05 by Umberto Marini Bettolo Marconi, U MARCONI, Andrea Puglisi +5 · 2 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Statistical Mechanics and Entropy #cond-mat.stat-mech #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.1016/j.physrep.2008.02.002
published as Physics Reports vol. 461, p. 111 (2008) · Review paper, 162 pages, in press on Physics Reports
arxiv created 2008/03/05 · openalex publication_date 2008/03/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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, nano-systems and biological systems.