Galilean relativity for Brownian dynamics and energetics

TL;DR

This study experimentally investigates how inertial reference frame changes affect overdamped Brownian motion and energetics, confirming weak Galilean invariance and deriving a Galilean invariant thermodynamic law.

Contribution

It provides experimental validation of weak Galilean invariance in Brownian dynamics and derives a Galilean invariant form of the stochastic thermodynamic first law.

Findings

Brownian dynamics remains weakly Galilean invariant.

Derived a Galilean invariant stochastic thermodynamic first law.

Discussed practical implications for force measurements in flows.

Abstract

We study experimentally the impact of inertial reference frame changes on overdamped Brownian motion. The reference frame changes are implemented by inducing, with a laser, laminar convection flows in a column of fluid where Brownian microspheres are dispersed. The convection flow plays the role of the relative velocity between the laboratory and the fluid comoving frames, and enables us to analyse the consequences of Galilean transformations on Brownian diffusion. We verify in particular how the Brownian dynamics remains "weakly" Galilean invariant, in agreement with recent discussions. We also carefully look at the consequences of Galilean relativity on the Brownian energetics. This leads us to derive a Galilean invariant expression of the stochastic thermodynamic first law, consistent with existing theoretical results. We finally discuss a potential ambiguity of the Galilean relativistic features of diffusive systems that has obvious practical implications in the context of force measurements in external flows.