Anisotropic isometric fluctuation relations in experiment and theory on a self-propelled rod

The isometric fluctuation relation (IFR) [P. I. Hurtado et al., Proc. Natl. Acad. Sci. USA 108, 7704 (2011)] relates the relative probability of current fluctuations of fixed magnitude in different spatial directions. We test its validity in an experiment on a tapered rod, rendered motile by vertical vibration and immersed in a sea of spherical beads. We analyze the statistics of the velocity vector of the rod and show that they depart significantly from the IFR of Hurtado et al. Aided by a Langevin-equation model we show that our measurements are largely described by an anisotropic generalization of the IFR [R. Villavicencio et al., Europhys. Lett. 105, 30009 (2014)], with no fitting parameters, but with a discrepancy in the prefactor whose origin may lie in the detailed statistics of the microscopic noise. The experimentally determined large-deviation function of the velocity vector has a kink on a curve in the plane.