Spectral fingerprints of non-equilibrium dynamics: The case of a Brownian gyrator

Abstract

The same system can exhibit a completely different dynamical behavior when it evolves in equilibrium conditions or when it is driven out-of-equilibrium by, e.g., connecting some of its components to heat baths kept at different temperatures. Here we concentrate on an analytically solvable and experimentally-relevant model of such a system -- the so-called Brownian gyrator -- a two-dimensional nanomachine that performs a systematic, on average, rotation around the origin under non-equilibrium conditions, while no net rotation takes place in equilibrium. On this example, we discuss a question whether it is possible to distinguish between two types of a behavior judging not upon the statistical properties of the trajectories of components, but rather upon their respective spectral densities. The latter are widely used to characterize diverse dynamical systems and are routinely calculated from the data using standard built-in packages. From such a perspective, we inquire whether the power spectral densities possess some "fingerprint" properties specific to the behavior in non-equilibrium. We show that indeed one can conclusively distinguish between equilibrium and non-equilibrium dynamics by analyzing the cross-correlations between the spectral densities of both components in the short frequency limit, or from the spectral densities of both components evaluated at zero frequency. Our analytical predictions, corroborated by experimental and numerical results, open a new direction for the analysis of a non-equilibrium dynamics.

23 pages, 6 figures

References in corpus (20)

• Fluctuation-Dissipation: Response Theory in Statistical Physics
• Fluctuations and response of nonequilibrium states
• A review of linear response theory for general differentiable dynamical systems
• Temperature in and out of equilibrium: a review of concepts, tools and attempts
• First passages for a search by a swarm of independent random searchers
• Experimental verification of a modified fluctuation-dissipation relation for a micron-sized particle in a non-equilibrium steady state
• The Brownian gyrator: a minimal heat engine on the nano-scale
• Spectral content of a single non-Brownian trajectory
• Experimental Realization of a Minimal Microscopic Heat Engine
• Microscopic theory for negative differential mobility in crowded environments
• Experimental Test of a New Equality: Measuring Heat Dissipation in an Optically Driven Colloidal System
• Quantitative analysis of non-equilibrium systems from short-time experimental data
• Inertial effects on the Brownian gyrator
• An autonomous out of equilibrium Maxwell's demon for controlling the energy fluxes produced by thermal fluctuations
• Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model
• Information-theoretic analysis of the directional influence between cellular processes
• Spectral density of individual trajectories of an active Brownian particle
• Current-mediated synchronization of a pair of beating non-identical flagella
• Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes
• Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes

Cited by in corpus (11)

• Inference in non-equilibrium systems from incomplete information: the case of linear systems and its pitfalls
• Nonequilibrium diffusion processes via non-Hermitian electromagnetic quantum mechanics with application to the statistics of entropy production in the Brownian gyrator
• Passive particle in an active bath: How can we tell it is out of equilibrium?
• Fractional Brownian Gyrator
• Cooperative dynamics in two-component out-of-equilibrium systems: Molecular "spinning tops"
• Experimental realization of an analog of entanglement between two Brownian particles
• Minimum time connection between non-equilibrium steady states: the Brownian gyrator
• Noise-to-signal ratio of single-trajectory spectral densities in centered Gaussian processes
• Frequency-frequency correlations of single-trajectory spectral densities of Gaussian processes
• Irregular gyration of a two-dimensional random-acceleration process in a confining potential
• Classification of diffusion processes in dimension $d$ via the Carleman approach with applications to models involving additive, multiplicative or square-root noises