Fluctuation formula and non-Gaussian distribution of the entropy production rate in the thermostated Lorentz gas

Abstract

In this paper we numerically examine the connection of the Gallavotti-Cohen fluctuation formula and the functional form of the corresponding probability density function in the field driven Lorentz gas thermostated by the Gaussian isokinetic thermostat. We analyze the moments of the entropy production rate fluctuations and show that all the central moments of the averaged fluctuations exhibit power law dependence on the length of the averaging time interval, indicating that this density deviates from a Gaussian. Furthermore the obtained exponents are found to obey a special pairing rule showing that the corresponding probability density function can not be scaled in the averaging time interval.