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.

(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.