Gaussian noise and time-reversal symmetry in non-equilibrium Langevin models

We solve the generalized Langevin equation driven by a stochastic force with power-law autocorrelation function. A stationary Markov process has been applied as a model of the noise. However, the resulting velocity variance does not stabilizes but diminishes with time. It is shown that algebraic distributions can induce such non-stationary affects. Results are compared to those obtained with a deterministic random force. Consequences for the diffusion process are also discuss...

This work is an analytical calculation of the path probability for random dynamics of mechanical system described by Langevin equation with Gaussian noise. The result shows an exponential dependence of the probability on the action. In the case of non dissipative limit, the action is the usual one in mechanics in accordance with the previous result of numerical simulation of random motion. In the case of dissipative motion, the action in the exponent of the exponential probab...

Nonergodic Brownian motion is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding either a vanishing or a divergent zero-frequency friction strength, the non-Markovian Browninan dynamics exhibits a riveting, anomalous diffusion behavior being characterized by a ballistic or possibly also a localized dynamics. As a consequence, such tailored thermal noise may cause a net acceleration of directed transport in a rocking Brownian motor...

We introduce a Langevin equation characterized by a time dependent drift. By assuming a temporal power-law dependence of the drift we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular diffusive, subdiffusive, superdiffusive and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmo...

Graham has shown in Z. Physik B 26, 397-405 (1977) that a fluctuation-dissipation relation can be imposed on a class of non-equilibrium Markovian Langevin equations that admit a stationary solution of the corresponding Fokker-Planck equation. The resulting equilibrium form of the Langevin equation is associated with a nonequilibrium Hamiltonian. Here we provide some explicit insight into how this Hamiltonian may loose its time reversal invariance and how the "reactive" and "d...

We report on novel Brownian, yet non-Gaussian diffusion, in which the mean square displacement of the particle grows linearly with time, the probability density for the particle spreading is Gaussian-like, however, the probability density for its position increments possesses an exponentially decaying tail. In contrast to recent works in this area, this behaviour is not a consequence of either a space or time-dependent diffusivity, but is induced by external non-thermal noise...

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce stabilization of otherwise diverging trajectories in dynamical systems. However, to identify how exactly this takes place in actual processes usually is not a simple task. Here we unveil a few trends leading to dynamical stabilization and diversity of ...

By studying a nonequilibrium Langevin system, we find that a simple condition determines the decomposition of the coarse-grained force into a dissipative force, an effective driving force and noise. From this condition, we derive a new universal inequality, $D \ge \gamma \mud^2 T$, relating the diffusion constant $D$, the differential mobility $\mud$, the bare friction constant $\gamma$ and the temperature $T$. Due to the general nature of the argument we present, we believe ...

We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gau...

We discuss how the first order Langevin equation for the overdamped dynamics of an interacting system has a natural time reversal of simple but surprising form, with consequences for correlation functions. This leads to the correlation of interactions as a strictly restraining term in the time-dependent diffusion tensor of the system, deriving the relation first suggested by Fixman. Applying this to the time-dependent diffusion of dilute polymer coils leads to the quantitativ...