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

We study transient work Fluctuation Relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the Fluctuation-Dissipation Relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the Fluctuation-Dissipation Relation of the...

Using a reverse-engineering approach on the time-distorted solution in a reference potential, we work out the external driving potential to be applied to a Brownian system in order to slow or accelerate the dynamics, or even to invert the arrow of time. By welding a direct and time-reversed evolution towards a well chosen common intermediate state, we derive analytically a smooth protocol to connect two \emph{arbitrary} states in an arbitrarily short amount of time. Not only ...

Deriving an arrow of time from time-reversal symmetric microscopic dynamics is a fundamental open problem in physics. Here we focus on several derivations of dissipative dynamics and the thermodynamic arrow of time to study precisely how time-reversal symmetry is broken in open classical and quantum systems. These derivations all involve the Markov approximation applied to a system interacting with an infinite heat bath. We find that the Markov approximation does not imply a ...

Based on the system heat bath approach where the bath is nonlinearly modulated by an external Gaussian random force, we propose a new microscopic model to study directed motion in the overdamped limit for a nonequilibrium open system. Making use of the coupling between the heat bath and the external modulation as a small perturbation we construct a Langevin equation with multiplicative noise and space dependent dissipation and the corresponding Fokker-Planck-Smoluchowski equa...

It is well known that path probabilities of Brownian motion correspond to the equilibrium configurational probabilities of flexible Gaussian polymers, while those of active Brownian motion correspond to in-extensible semiflexible polymers. Here we investigate the properties of the equilibrium polymer that corresponds to the trajectories of particles acted on simultaneously by both Brownian as well as active noise. Through this mapping we can see interesting crossovers in mech...

We explore the motion of a classical particle in a symmetric potential with non-Gaussian skewed white noise. We show analytically and numerically that the presence of nonzero odd moments leads to a macroscopic current. For a noise with a vanishing third moment we find that the current changes sign as the potential or the noise strength is increased. Possible physical situations are discussed including motor-protein motion and driven systems like fluidized beds.

We develop a field-theoretic perturbation method preserving the fluctuation-dissipation relation (FDR) for the dynamics of the density fluctuations of a noninteracting colloidal gas plunged in a quenched Gaussian random field. It is based on an expansion about the Brownian noninteracting gas and can be considered and justified as a low-disorder or high-temperature expansion. The first-order bare theory yields the same memory integral as the mode-coupling theory (MCT) develope...

We propose a new approach concerning the introduction of time-irreversibility in statistical mechanics. It is based on a transition function defined in terms of path integral and verifying a time-irreversible equation. We show first how dynamic processes may enter in the description of equilibrium states. In order to do that a characteristic time is associated with closed paths. For large isolated systems at equilibrium or for systems in contact with a thermostat our results ...

A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained.

The properties of the thermal force driving micron particles in incompressible fluids are studied within the hydrodynamic theory of the Brownian motion. It is shown that the assumption used for the hydrodynamic Langevin equation in its usual form, according to which the random force at a time t and the velocity of the particle at the initial time equal to zero are uncorrelated, leads to super-diffusion of the particle. To obtain the correct Einstein diffusion at long times, t...