# Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

## TL;DR

This paper extends the linear response theory to nonequilibrium inertial systems, showing the response decomposes into entropic and frenetic parts linked to time-reversal symmetry, with implications for modified Einstein relations.

## Contribution

It provides a generalized response formula for inertial nonequilibrium systems, incorporating dynamical activity and extending previous equilibrium-based results.

## Key findings

- Response decomposes into entropic and frenetic correlations.
- The response involves an excess in dynamical activity.
- Modified Einstein relation includes a correlation term.

## Abstract

We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.