In
these two lectures I shall discuss:
(1) The definition of `effective temperatures' through the
modification of the fluctuation-dissipation relation between induced
and spontaneous fluctuations. Their behaviour in systems evolving in
several different time-scales, their thermodynamic properties, their
relation to a microcanonical definition, and their relevance for the
space-time fluctuations.
(2) An extension of the fluctuation theorem to stochastic models that,
in the limit of zero external drive, are not able to equilibrate with
their environment. In this context I shall show that the probability
distribution function of a suitably defined entropy production rate
verifies the Fluctuation Relation with the ambient temperature
replaced by the (frequency-dependent) effective temperature.