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.
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