Fluctuation-response relation for a nonequilibrium system with resolved Markovian embedding

TL;DR

This study demonstrates that the fluctuation-response relation for nonequilibrium systems with non-Markovian dynamics can be accurately restored by explicitly resolving the Markovian embedding, validated through experiments with a colloidal particle.

Contribution

The paper provides experimental evidence that the fluctuation-response relation can be recovered in nonequilibrium non-Markovian systems by explicitly considering the Markovian embedding.

Findings

Fluctuation-response relations are violated in reduced non-Markovian dynamics.

Explicit Markovian embedding restores the fluctuation-response relation.

Response is determined by steady-state correlations involving the conjugate observable.

Abstract

Fluctuation-response relations must be modified to describe nonequilibrium systems with non-Markovian dynamics. Here, we experimentally demonstrate that such relation is quantitatively recovered when the appropriate Markovian embedding of the dynamics is explicitly resolved. Using a colloidal particle optically trapped in a harmonic potential and driven out of equilibrium by a controlled colored noise, we study the response to a perturbation of the stiffness of the confining potential. While the reduced dynamics violates equilibrium fluctuation-response relations, we show that the dynamical response to the stiffness perturbation is fully determined by steady-state correlations involving the exact conjugate observable in the Markovian embedding.