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Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod

The Isometric Fluctuation Relation (IFR) [P.I. Hurtado et al., PNAS 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 analyse 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., EPL 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.