Fluctuation theorem, non linear response and the regularity of time reversal symmetry

The Gallavotti-Cohen fluctuation theorem (FT) implies an infinite set of identities between correlation functions that can be seen as a generalization of Green-Kubo formula to the nonlinear regime. As an application, we discuss a perturbative check of the FT relation through these identities for a simple Anosov reversible system; we find that the lack of differentiability of the time reversal operator implies a violation of the Gallavotti-Cohen fluctuation relation. Finally, a brief comparison to Lebowitz-Spohn FT is reported. (C) 2010 American Institute of Physics. [doi:10.1063/1.3396283]