Identities for nonlinear memory kernels

TL;DR

This paper derives identities for nonlinear memory kernels in systems far from equilibrium, based on local detailed balance, and tests these identities through simulations of driven Brownian particles.

Contribution

It introduces new identities for nonlinear memory kernels in non-equilibrium systems, extending the fluctuation dissipation theorem to nonlinear regimes.

Findings

Identities are validated in simulations of driven Brownian particles.

The identities include the fluctuation dissipation theorem as a special case.

Series relations for non-equilibrium cumulants are established.

Abstract

Perturbing a system far away from equilibrium via a time dependent protocol can formally be described by a nonlinear Volterra series expansion. Here we derive identities for the nonlinear memory kernels arising in such nonlinear expansion, including the possibility of a nonlinear coupling between perturbation and system. These identities rely on local detailed balance, and they include the fluctuation dissipation theorem as the lowest order identity. We test them in simulations for driven over- and underdamped Brownian particles. These identities for memory kernels can be recast in a series relation for the non-equilibrium cumulants of the observable conjugate to the driving and the observable described by the Volterra series.