Fluctuation relations for anisotropic systems

¹ School of Mathematical Sciences, Queen Mary University of London - London E1 4NS, UK
² National Institute for Theoretical Physics (NITheP) - Stellenbosch 7600, South Africa
³ Institute of Theoretical Physics, University of Stellenbosch - Stellenbosch 7600, South Africa

Received: 14 November 2013
Accepted: 27 January 2014

Abstract

Currents of particles or energy in driven non-equilibrium steady states are known to satisfy certain symmetries, referred to as fluctuation relations, determining the ratio of the probabilities of positive fluctuations to negative ones. A generalization of these fluctuation relations has been proposed recently for extended non-equilibrium systems of dimension greater than one, assuming, crucially, that they are isotropic (Hurtado P. I., Pérez-Espigares C., del Pozo J. J. and Garrido P. L., Proc. Natl. Acad. Sci. U.S.A., 108 (2011) 7704). Here we relax this assumption and derive a fluctuation relation for d-dimensional systems having anisotropic bulk driving rates. We test the validity of this anisotropic fluctuation relation by calculating the particle current fluctuations in the 2d anisotropic zero-range process, using both exact and fluctuating hydrodynamic approaches.