In this paper we examine numerically the Gallavotti-Cohen fluctuation formula for phase-space contraction rate and entropy production rate fluctuations in the Nosé-Hoover thermostated periodic Lorentz gas. Our results indicate that while the phase-space contraction rate fluctuations violate the fluctuation formula near equilibrium states, the entropy production rate fluctuations obey this formula near and far from equilibrium states as well.

We investigate numerically the validity of the Gallavotti-Cohen fluctuation formula in the two and three dimensional periodic Lorentz gas subjected to constant electric and magnetic fields and thermostated by the Gaussian isokinetic thermostat. The magnetic field breaks the time reversal symmetry, and by choosing its orientation with respect to the lattice one can have either a generalized reversing symmetry or no reversibility at all. Our results indicate that the scaling property described by the fluctuation formula may be approximately valid for moderately large fluctuations even in the absence of reversibility.The Lorentz gas (LG) thermostated by a Gaussian isokinetic (GIK) thermostat is one of the most popular models in the study of the relationship between transport properties and chaotic behaviour in nonlinear dynamical systems. Since the microscopic dynamics of the LG is chaotic, and on a sufficiently long time scales it possesses a well defined macroscopic transport coefficient, it can be used to study the connection of microscopic chaos and macroscopic nonequilibrium behaviour.The so-called fluctuation formula (FF) has first been observed numerically in a system of thermostated fluid particles undergoing shear flow [1]. In that model, trajectory segments violating the second law of thermodynamics were found with probabilities exponentially smaller than those of trajectory segments associated with normal thermodynamical behaviour. More precisely, let ξ τ (t) denote the entropy production rate ξ averaged over a time interval of length τ centered around time t: ξ τ (t) =

We demonstrate that in the thermostatted three-dimensional Lorentz gas the symmetry of the Lyapunov spectrum can be broken by adding to the system an external magnetic field not perpendicular to the electric field. For perpendicular field vectors, there is a Hamiltonian reformulation of the dynamics and the conjugate pairing rule still holds. This indicates that symmetric Lyapunov spectra has nothing to do with time reversal symmetry or reversibility; instead, it seems to be related to the existence of a Hamiltonian connection.