# Conduction at the onset of chaos

## TL;DR

This paper explores how conductive processes behave at the transition to chaos, linking microscopic dynamics with transport properties, and revealing complex relaxation patterns at the chaos onset.

## Contribution

It introduces observables connecting diffusion with microscopic dynamics and analyzes transport behavior at the onset of chaos, extending Onsager's framework to non-reversible systems.

## Key findings

- Monotonic relaxation in chaotic regimes
- Complex relaxation patterns at chaos onset
- Analytical and numerical solutions for Brownian particles

## Abstract

After a general discussion of the thermodynamics of conductive processes, we introduce specific observables enabling the connection of the diffusive transport properties with the microscopic dynamics. We solve the case of Brownian particles, both analytically and numerically, and address then whether aspects of the classic Onsager's picture generalize to the non-local non-reversible dynamics described by logistic map iterates. While in the chaotic case numerical evidence of a monotonic relaxation is found, at the onset of chaos complex relaxation patterns emerge.