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 over time T we count the difference (Nℓ − Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. 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.
Highlights
Fluctuation relations have emerged from an analysis of entropy production in driven dissipative processes
It was found that such symmetries are an expression of local detailed balance, implying that the total path-wise entropy flux is the source term of time-reversal breaking in the nonequilibrium action governing the dynamical ensemble; see [3, 4, 5, 6, 7]
When measuring the differences in dynamical activity in (5.1) one obtains asymmetric statistics arising from the density profile in the slab, which is shaped by the nonequilibrium condition set by the reservoirs
Summary
Fluctuation relations have emerged from an analysis of entropy production in driven dissipative processes. Since a new wave of research interest on a specific time-symmetric quantity, the dynamical activity, has emerged [15, 16, 17, 18] This dynamical activity, or frenesy as called in the context of linear response [18], captures essential nonequilibrium kinetic aspects. In the present paper differences in dynamical activity between the various contacts of the system with the environment arise from the breaking of a spatial symmetry that naturally accompanies the nonequilibrium situation. The main result of this paper (in Section 4) gives fluctuation symmetries in terms of a difference in dynamical activities. We derive in these models the active fluctuation symmetries for differences in dynamical activity (between the left versus right edge of the system). The computer simulations we present validate our guesses in the non-Gaussian fluctuation sector
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