We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by the Green-Kubo relation. Next we show that the law of the empirical average current satisfies a large deviations principle and compute explicitly the rate functional in a suitable scaling limit. We observe that this functional is not strictly convex. © 2011 American Institute of Physics.
Large deviations of the current in stochastic collisional dynamics / Raphaël, Lefevere; Mariani, Mauro; Lorenzo, Zambotti. - In: JOURNAL OF MATHEMATICAL PHYSICS. - ISSN 0022-2488. - STAMPA. - 52:3(2011), pp. 033302-033323. [10.1063/1.3567169]
Large deviations of the current in stochastic collisional dynamics
MARIANI, Mauro;
2011
Abstract
We consider a class of deterministic local collisional dynamics, showing how to approximate them by means of stochastic models and then studying the fluctuations of the current of energy. We show first that the variance of the time-integrated current is finite and related to the conductivity by the Green-Kubo relation. Next we show that the law of the empirical average current satisfies a large deviations principle and compute explicitly the rate functional in a suitable scaling limit. We observe that this functional is not strictly convex. © 2011 American Institute of Physics.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.