# Thermal response of a Fermi-Pasta-Ulam chain with Andersen thermostats

## TL;DR

This paper develops a fluctuation-response relation for the thermal response of Fermi-Pasta-Ulam chains with Andersen thermostats, enabling better predictions of thermal properties out of equilibrium.

## Contribution

It introduces a novel fluctuation-response relation for inertial heat conducting systems driven out of equilibrium using Andersen thermostats.

## Key findings

- The relation predicts thermal expansion and heat capacity more accurately than small perturbation methods.
- Simulations confirm improved susceptibility estimates with the new relation.
- The approach extends linear response theory to nonequilibrium inertial systems.

## Abstract

The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi-Pasta-Ulam (FPU) model driven by two different boundary temperatures. For models of inertial systems out of equilibrium, including relaxing systems, we show that Andersen thermostats are a natural tool for studying the thermal response. We derive a fluctuation-response relation that allows to predict thermal expansion coefficients or the heat capacitance in nonequilibrium regimes. Simulations of the FPU chain of oscillators suggest that estimates of susceptibilities obtained with our relation are better than those obtained via a small perturbation.