Fluctuation-Dissipation: Response Theory in Statistical Physics
Physics Reports, (2008)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, nano-systems and biological systems.