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 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.
Highlights
The laws of classical mechanics are written in inertial reference frames, interconnected by Galilean transformations (GT) that ensure the invariance of the acceleration
We have verified experimentally the principle of “weak” Galilean invariance (GI) for coarse-grained diffusive systems, and we have derived the expressions for the stochastic energetics production rates and the associated probability density functions that yield a frame invariant formulation of the first law
We emphasized the crucial importance of recognizing in the drift term the signature of a Galilean transform in order not to interpret it as an external force field acting on the colloidal ensemble
Summary
The laws of classical mechanics are written in inertial reference frames, interconnected by Galilean transformations (GT) that ensure the invariance of the acceleration. The problem resides precisely in the fact that this viewpoint leads, as we just showed, to a totally wrong energetic balance It remains problematic as long as one models in the laboratory reference frame diffusion and transport by an external force field, without having recognized before hand the comoving frame in which the analysis must be set, with a drift term properly treated in relation with GT. (13-15) gives a striking illustration of the energetic consequences of assigning to the drift term the role of an external force rather than treating it as induced by a change of reference frame These discrepancies correspond to the fundamental ambiguity in the interpretation of the trajectories measured in the laboratory frame and displayed in Fig. 5 (ac).
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