# Nonequilibrium corrections to gradient flow

## TL;DR

This paper explains how nonequilibrium media induce nongradient forces on probes, highlighting the role of excess frenesy and entropy flux in response to system changes.

## Contribution

It provides a detailed response theory elucidating the mechanism behind nongradient forces in nonequilibrium systems, focusing on the interplay of frenesy and entropy flux.

## Key findings

- Nongradient forces arise due to a systematic twist of excess frenesy.
- The mechanism is linked to the response of the system to coupling and position changes.
- Theoretical framework clarifies the origin of nongradient effects in nonequilibrium media.

## Abstract

The force on a probe induced by a nonequilibrium medium is in general nongradient. We detail the mechanism of that feature via nonequilibrium response theory. The emergence of nongradient forces is due to a systematic "twist" of the excess frenesy with respect to the entropy flux, in response to changes in the coupling or in the position of the probe in the nonequilibrium medium.