 1070 A.C.D. van Enter, R. Fern\'andez, Fr.den Hollander and F.Redig
 A largedeviation view on dynamical GibbsnonGibbs transitions
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May 2, 10

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Abstract. We develop a spacetime largedeviation point of view on
GibbsnonGibbs transitions in spin systems subject to a stochastic spinflip dynamics. Using the general theory for large deviations of functionals of Markov processes outlined in Feng and Kurtz [11], we
show that the trajectory under the spinflip dynamics of the empirical measure of the spins in a large block in Z^d satisfies a large deviation principle in the limit as the block size tends to infinity. The associated rate function can be computed as the action functional
of a Lagrangian that is the Legendre transform of a certain nonlinear generator, playing a role analogous to the momentgenerating function in the GaertnerEllis theorem of large deviation theory when this is applied to finitedimensional Markov processes. This rate
function is used to define the notion of bad empirical measures , which are the discontinuity points of the optimal trajectories (i.e., the trajectories minimizing the rate function) given the empirical measure at the end of the trajectory. The dynamical GibbsnonGibbs
transitions are linked to the occurrence of bad empirical measures: for short times no bad empirical measures occur, while for intermediate and large times bad empirical measures are possible. A future research program is proposed to classify the various possible scenarios behind this crossover, which we refer to as a natureversusnurture transition.
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