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

TL;DR

This paper demonstrates that spectral density analysis can reliably distinguish between equilibrium and non-equilibrium dynamics in a Brownian gyrator, revealing specific spectral fingerprints of non-equilibrium behavior.

Contribution

It introduces a spectral density-based method to identify non-equilibrium dynamics, validated through analytical, experimental, and numerical results.

Findings

Spectral densities at zero and low frequencies serve as fingerprints of non-equilibrium behavior.

Cross-correlations of spectral densities can distinguish equilibrium from non-equilibrium states.

Analytical predictions are supported by experimental and numerical data.

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.