# The underdamped Brownian duet and stochastic linear irreversible thermodynamics

## TL;DR

This paper introduces the underdamped Brownian duet as a model for dissipative systems and work-to-work engines, illustrating recent stochastic thermodynamics concepts through analytic and simulation methods.

## Contribution

It presents a new prototype model that exemplifies key principles of stochastic thermodynamics, including symmetry relations and efficiency trade-offs.

## Key findings

- Demonstrates Onsager-Casimir symmetry in the model
- Analyzes power, efficiency, and dissipation trade-offs
- Provides explicit analytic calculations and Langevin simulations

## Abstract

Building on our earlier work (Proesmans et. al., Phys.~Rev.~X \textbf{6} (2016), 041010), we introduce the underdamped Brownian duet as a prototype model of a dissipative system or of a work-to-work engine. Several recent advances from the theory of stochastic thermodynamics are illustrated with explicit analytic calculations and corresponding Langevin simulations. In particular, we discuss Onsager-Casimir symmetry, the trade-off relations between power, efficiency and dissipation, and stochastic efficiency.