Linear response in the nonequilibrium zero range process

TL;DR

This paper investigates the linear response of the boundary driven zero range process in nonequilibrium conditions, highlighting the roles of entropic and frenetic contributions and extending classical relations like Green-Kubo.

Contribution

It introduces a decomposition of the linear response into entropic and frenetic parts, revealing kinetic effects in nonequilibrium regimes and modifying traditional response formulas.

Findings

Response decomposes into entropic and frenetic contributions.

Frenetic effects influence the response at boundaries.

Nonlinear modifications to Green-Kubo relation.

Abstract

We explore a number of explicit response formulae around the boundary driven zero range process to changes in the exit and entrance rates. In such a nonequilibrium regime kinetic (and not only thermodynamic) aspects make a difference in the response. Apart from a number of formal approaches, we illustrate a general decomposition of the linear response into entropic and frenetic contributions, the latter being realized from changes in the dynamical activity at the boundaries. In particular, in this way one obtains nonlinear modifications to the Green-Kubo relation. We end by bringing some general remarks about the situation where that nonequilibrium response remains given by the (equilibrium) Kubo formula such as for the density profile in the boundary driven Lorentz gas.