The fluctuation theorem (FT) for stochastic dynamics, as presented by Jorge Kurchan, addresses the distribution of entropy production over long time intervals. It states that the ratio of probabilities of having a given entropy production σ_t to that of having -σ_t is e^{tσ_t}. This theorem was originally formulated for thermostated Hamiltonian systems under certain chaoticity assumptions. The paper demonstrates how to derive the Gallavotti-Cohen (GC) fluctuation theorem for systems undergoing Langevin dynamics, highlighting its simplicity and the bypassing of non-trivial ergodic theory issues. The FT is shown to reduce to the fluctuation-dissipation and Onsager relations in the equilibrium limit. The paper also discusses the nonlinear fluctuation-dissipation theorem for equilibrium systems perturbed by strong fields. It explores the implications of the FT in systems with infinitely many degrees of freedom, noting that the theorem may be violated in such systems. The paper also presents a direct proof of the nonlinear fluctuation-dissipation theorem for Langevin processes without inertial terms, corresponding to the Fokker-Planck equation. The results are applied to various driven systems, including Burgers-KPZ, phase-separation under shear, and turbulence. The paper concludes that the violation of the FT in infinite systems may indicate complex dynamics, suggesting that the FT might play a similar role in strongly driven infinite systems as it does in finite ones.The fluctuation theorem (FT) for stochastic dynamics, as presented by Jorge Kurchan, addresses the distribution of entropy production over long time intervals. It states that the ratio of probabilities of having a given entropy production σ_t to that of having -σ_t is e^{tσ_t}. This theorem was originally formulated for thermostated Hamiltonian systems under certain chaoticity assumptions. The paper demonstrates how to derive the Gallavotti-Cohen (GC) fluctuation theorem for systems undergoing Langevin dynamics, highlighting its simplicity and the bypassing of non-trivial ergodic theory issues. The FT is shown to reduce to the fluctuation-dissipation and Onsager relations in the equilibrium limit. The paper also discusses the nonlinear fluctuation-dissipation theorem for equilibrium systems perturbed by strong fields. It explores the implications of the FT in systems with infinitely many degrees of freedom, noting that the theorem may be violated in such systems. The paper also presents a direct proof of the nonlinear fluctuation-dissipation theorem for Langevin processes without inertial terms, corresponding to the Fokker-Planck equation. The results are applied to various driven systems, including Burgers-KPZ, phase-separation under shear, and turbulence. The paper concludes that the violation of the FT in infinite systems may indicate complex dynamics, suggesting that the FT might play a similar role in strongly driven infinite systems as it does in finite ones.