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We report the breaking of ergodicity for a class of generalized, Brownian motion obeying a non-Markovian dynamics being driven by a generalized Langevin equation (GLE). This very feature originates from a vanishing of the effective friction. A novel quantity b (being uniquely determined from the corresponding memory friction kernel gamma(t)of the GLE) is introduced as a parameter that is capable of measuring the strength of ergodicity breaking. The ergodicity breaking is accompanied by a nonunique stationary probability density for the corresponding embedded Markovian dynamics. Differing physical situations for a Brownian, non-Markovian particle dynamics occurring either in free Brownian motion, in a periodic potential, or in a confining potential are elucidated.

The dynamics of water inside nanochannels is of great importance for biological activities as well as for the design of molecular sensors, devices, and machines, particularly for sea water desalination. When confined in specially sized nanochannels, water molecules form a single-file structure with concerted dipole orientations, which collectively flip between the directions along and against the nanotube axis. In this paper, by using molecular dynamics simulations, we observed a net flux along the dipole-orientation without any application of an external electric field or external pressure difference during the time period of the particular concerted dipole orientations of the molecules along or against the nanotube axis. We found that this unique special-directional water transportation resulted from the asymmetric potential of water-water interaction along the nanochannel, which originated from the concerted dipole orientation of the water molecules that breaks the symmetry of water orientation distribution along the channel within a finite time period. This finding suggests a new mechanism for achieving high-flux water transportation, which may be useful for nanotechnology and biological applications.

We present a thermal broadband noise from the difference between two Ornstein-Uhlenbeck noises, which can induce a ballistic diffusion, i.e., long-time mean square displacement of a free particle driven by this noise reads proportional to t(2). We apply this noise to a flashing ratchet and the mean velocity of the particle is calculated via Langevin simulation. The results show that a double peak of the mean velocity and flux reversal appears for the ratchet with large and small asymmetries, respectively; the inertia effect induces a large mean velocity and multireversal of flux. These rich and interesting phenomena are explained.

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