Fluctuation–dissipation: Response theory in statistical physics

• Published in: Physics reports Vol. 461; no. 4; pp. 111 - 195
• Main Authors: Marconi, Umberto Marini Bettolo, Puglisi, Andrea, Rondoni, Lamberto, Vulpiani, Angelo
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.06.2008; Elsevier Science
• Subjects: Correlation functions; Exact sciences and technology; Fluctuation relations; Large deviations; Nonequilibrium phenomena; Physics; 05.40.-a; 45.70.-n; Large deviations; Correlation functions; Nonequilibrium phenomena; 47.52.+j; 05.70.Ln; 02.50.Ga; 51.20.+d; 47.27.eb; 47.27.-i; 05.60.-k; Fluctuation relations; Brownian motion; Relaxation; Fluctuations; Hamiltonians; Statistical physics; Statistical theory; Disturbances; Linear theory; Hamiltonian mechanics; 05.40.-a;05.70.Ln;45.70.-n;47.52.+j;02.50.Ga;05.60.-k;47.27.-i;47.27.eb;51.20.+d;Correlation functions;Nonequilibrium phenomena;Large deviations;Fluctuation relations; Statistical mechanics; Large deviation
• ISSN: 0370-1573; 1873-6270
• DOI: 10.1016/j.physrep.2008.02.002

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.