The role of the nature of the noise in the thermal conductance of mechanical systems

TL;DR

This paper investigates how the type of noise, specifically Lévy-Itô versus white noise, influences the thermal conductance in small coupled oscillator systems, revealing independence in linear cases and mixing effects in nonlinear cases.

Contribution

It demonstrates that the nature of noise affects thermal conductance differently in linear and nonlinear coupled systems, highlighting the importance of noise composition in thermomechanical properties.

Findings

White noise's Lévy-Itô composition is irrelevant for linear systems' conductance.

In nonlinear systems, noise type influences the coupling of mechanical and thermodynamical properties.

Explicit noise definition becomes crucial in nonlinear coupling scenarios.

Abstract

Focussing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the thermal conductance. For white noises, we prove that the L\'evy-It\^o composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a non-equilibrium linearly coupled chain, which signals the independence between mechanical and thermodynamical properties. On the other hand, for the non-linearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role.