General aspects of the Fluctuation-Dissipation Relation (
FDR), and Response The-
ory are considered. After analyzing the conceptual and hist
orical relevance of fluc-
tuations in statistical mechanics, we illustrate the relat
ion between the relaxation of
spontaneous fluctuations, and the response to an external pe
rturbation. These stud-
ies date back to Einstein’s work on Brownian Motion, were con
tinued by Nyquist
and Onsager and culminated in Kubo’s linear response theory
.
The FDR has been originally developed in the framework of sta
tistical mechanics
of Hamiltonian systems, nevertheless a generalized FDR hol
ds 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 Fluc
tuation Relations
(FR) concerning far from equilibrium systems. The connecti
on of these works with
large deviation theory is analyzed.
Some examples, beyond the standard applications of statist
ical mechanics, where
fluctuations play a major role are discussed: fluids, granula
r media, nano-systems
and biological systems. |