On the Fluctuation Law(s) for Hamiltonian systems (with equilibrium steady state): A Comment on cond-mat/0008421

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A generalization of the fluctuation law (FL) ("theorem"), formulated in 1993 by Evans, Cohen and Morriss for a nonequilibrium steady state, on the chaotic Hamiltonian systems with equilibrium steady state in recent publication ba Evans, Searles and Mittag (cond-mat/0008421) is briefly discussed. We argue that the physical meaning of this law, as presented in the latter publication, is qualitatively different from the original one. Namely, the original FL concerns the local (in time) fluctuations with an intriguing result: a high probability for the "violation" of the Second Law. Instead, the new law describes the global fluctuations for which this remarkable unexpected phenomenon is absent or hidden. We compare both types in both classes of Hamiltonian systems, and discuss remarkable similarities as well as the interesting distinctions.