Galilean relativity for Brownian dynamics and energetics

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 Cairoli et al (2018 Proc. Natl Acad. Sci. USA 115 5714). 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 Speck et al (2008 Phys. Rev. Lett. 100 178302). 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.