  We study the Fluctuation Theorem (FT) for entropy production in chaotic
discrete-time dynamical systems on compact metric spaces, and extend it to
empirical measures, all continuous potentials, and all weak Gibbs states. In
particular, we establish the FT in the phase transition regime. These results
hold under minimal chaoticity assumptions (expansiveness and specification) and
require no ergodicity conditions. They are also valid for systems that are not
necessarily invertible and involutions other than time reversal. Further
extensions involve asymptotically additive potential sequences and the
corresponding weak Gibbs measures. The generality of these results allows to
view the FT as a structural facet of the thermodynamic formalism of dynamical
systems.
