# Phononic heat transport in nanomechanical structures: steady-state and pumping

## TL;DR

This paper develops a phase space Green's function approach to analyze phononic heat transport in nanomechanical systems, capturing atomic details and non-equilibrium effects, including steady-state and driven conditions.

## Contribution

It introduces a novel formalism for phononic heat transport that accurately describes small molecular junctions and accounts for non-stationary and quantum thermodynamic properties.

## Key findings

- Correctly recovers Landauer-like heat conductance in steady state
- Derives expressions for non-stationary heat currents under periodic driving
- Applies formalism to diatomic molecular junctions

## Abstract

We study the heat transport due to phonons in nanomechanical structures using a phase space representation of non-equilibrium Green's functions. This representation accounts for the atomic degrees of freedom making it particularly suited for the description of small (molecular) junctions systems. We show that for the steady state limit our formalism correctly recovers the heuristic Landauer-like heat conductance for a quantum coherent molecular system coupled to thermal reservoirs. We find general expressions for the non-stationary heat current due to an external periodic drive. In both cases we discuss the quantum thermodynamic properties of the systems. We apply our formalism to the case of a diatomic molecular junction.