Active Fluctuation Symmetries

Abstract

In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary driven particle systems such as the open Kawasaki lattice gas and the zero range model. As a measure of time-symmetric dynamical activity we take the difference $(N_1-N_L)/T$ in the number of particles entering or leaving the system at the left versus the right edge of the system over time $T$. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.

20 pages, 3 figures

References in corpus (5)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Fluctuation theorems for stochastic dynamics
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• An expression for stationary distribution in nonequilibrium steady state
• Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems

Cited by in corpus (5)

• Uncertainty relations for underdamped Langevin dynamics
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Fluctuation theorems without time-reversal symmetry
• Symmetry-induced fluctuation relations for dynamical observables irrespective of their behaviour under time-reversal
• Spectral signatures of symmetry-breaking dynamical phase transitions