Fractional Brownian Gyrator

TL;DR

This paper analyzes a fractional Brownian gyrator model, revealing how long-range correlated noise influences the non-equilibrium steady state and persistent rotation in a nano-machine, with analytical and numerical insights.

Contribution

It introduces a fractional Gaussian noise-driven model of a nano-machine, providing analytical characterization of its non-equilibrium steady state and rotational behavior.

Findings

Persistent rotation occurs when noise differs across directions.

Analytical expressions for steady-state probability density and current are derived.

Numerical results support the analytical findings.

Abstract

When a physical system evolves in a thermal bath at a constant temperature, it arrives eventually to an equilibrium state whose properties are independent of the kinetic parameters and of the precise evolution scenario. This is generically not the case for a system driven out of equilibrium which, on the contrary, reaches a steady-state with properties that depend on the full details of the dynamics such as the driving noise and the energy dissipation. How the steady state depends on such parameters is in general a non-trivial question. Here, we approach this broad problem using a minimal model of a two-dimensional nano-machine, the Brownian gyrator, that consists of a trapped particle driven by fractional Gaussian noises -- a family of noises with long-ranged correlations in time and characterized by an anomalous diffusion exponent $\alpha$. When the noise is different in the different spatial directions, our fractional Brownian gyrator persistently rotates. Even if the noise is non-trivial, with long-ranged time correlations, thanks to its Gaussian nature we are able to characterize analytically the resulting nonequilibrium steady state by computing the probability density function, the probability current, its curl and the angular velocity and complement our study by numerical results.