# Nonlinear transport coefficients from large deviation functions

## TL;DR

This paper presents a novel method to compute high-order nonlinear transport coefficients in stochastic systems using large deviation theory, linking response to equilibrium correlations and enabling efficient evaluation.

## Contribution

It introduces a thermodynamic-like relation for nonlinear response based on large deviation functions, applicable to complex nanoscale systems.

## Key findings

- Successfully predicts transport coefficients in single particle systems.
- Demonstrates efficiency in systems with thermal rectification.
- Establishes a practical route for nonlinear response evaluation.

## Abstract

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to compute arbitrarily high order transport coefficients of stochastic systems, using the framework of large deviation theory. Leveraging time reversibility in the microscopic dynamics, we relate nonlinear response to equilibrium multi-time correlation functions among both time reversal symmetric and asymmetric observables, which can be evaluated from derivatives of large deviation functions. This connection establishes a thermodynamic-like relation for nonequilibrium response and provides a practical route to its evaluation, as large deviation functions are amenable to importance sampling. We demonstrate the generality and efficiency of this method in predicting transport coefficients in single particle systems and an interacting system exhibiting thermal rectification.