Exact time-averaged thermal conductance for small systems: Comparison between direct calculation and Green-Kubo formalism

TL;DR

This paper compares direct calculation and Green-Kubo formalism for exact thermal conductance in a low-dimensional system, confirming both methods yield identical results and providing an exact steady state distribution.

Contribution

It demonstrates the equivalence of direct and Green-Kubo methods for calculating thermal conductance in a specific low-dimensional system and derives an exact steady state distribution.

Findings

Both methods produce identical thermal conductance results.

Exact steady state probability distribution obtained.

Validation of Green-Kubo approach for this system.

Abstract

In this paper, we study exactly the thermal conductance for a low dimensional system represented by two coupled massive Brownian particles, both directly and via a Green-Kubo expression. Both approaches give exactly the same result. We also obtain exactly the steady state probability distribution for that system by means of time-averaging.