Abstract
We discuss 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, extending earlier results of Sellitto. We show that if the entropy production rate is suitably defined, its probability distribution function verifies the fluctuation relation with the ambient temperature replaced by a (frequency dependent) effective temperature. We derive modified Green–Kubo relations. We illustrate these results with the simple example of an oscillator coupled to a non-equilibrium bath driven by an external force. We discuss the relevance of our results for driven glasses and the diffusion of Brownian particles in out-of-equilibrium media and propose a concrete experimental strategy for measuring the low frequency value of the effective temperature using the fluctuations of the work done by an ac conservative field. We compare our results to related ones that appeared in the literature recently.