The Fluctuation Theorem as a

Common ground to recent studies exploiting relations between dynam-ical systems and non-equilibrium statistical mechanics is, so we argue, the standard Gibbs formalism applied on the level of space-time histories. The assumptions (chaoticity principle) underlying the Gallavotti-Cohen uctuation theorem make it possible, using symbolic dynamics, to employ the theory of one-dimensional lattice spin systems. The Kurchan and Lebowitz-Spohn analysis of this uctuation theorem for stochastic dynamics can be restated on the level of the space-time measure which is a Gibbs measure for an interaction determined by the transition probabilities. In this note we understand the uctuation theorem as a Gibbs property as it follows from the very deenition of Gibbs state. We give a local version of the uctuation theorem in the Gibbsian context and we derive from this a version also for some class of spatially extended stochastic dynamics. 1 Context and main observations. The uctuation theorem of Gallavotti and Cohen, see 10, 11, 26], asserts that for a class of dynamical systems the uctuations in time of the phase space contraction rate obey a general law. We refer to the cited literature for additional details and precision and we only sketch here the main ingredients. One considers a reversible smooth dynamical system ! (); 2. The phase space is in some sense bounded carrying only a nite number of degrees of freedom (a compact and connected manifold). The transformation Onderzoeksleider FWO, Flanders.