Stochastic thermodynamics of inertial-like Stuart-Landau dimer

TL;DR

This paper extends the Stuart-Landau dimer model to include inertia and noise, revealing new bistable phases and analyzing its thermodynamics, showing coherence enhances work output in a thermal machine.

Contribution

It introduces an inertial-like term into the Stuart-Landau dimer model and develops a stochastic thermodynamic framework for it, highlighting the role of synchronization in work output.

Findings

Bistable phase emerges without noise, with coexistence of coherent and incoherent limit cycles.

Thermodynamic observables like work show bistability in metastable regimes at finite temperature.

Coherent synchronization maximizes work output, acting as a reliable thermal machine.

Abstract

Stuart-Landau limit-cycle oscillators are a paradigm in the study of coherent and incoherent limit cycles. In this work, we generalize the standard Stuart-Landau dimer model to include effects due to an inertia-like term and noise and study its dynamics and stochastic thermodynamics. In the absence of noise (zero-temperature limit), the dynamics show the emergence of a new bistable phase where coherent and incoherent limit cycles coexist. At finite temperatures, we develop a stochastic thermodynamic framework based on the dynamics of a charged particle in a magnetic field to identify physically meaningful heat and work. The stochastic system no longer exhibits the bistable phase but the thermodynamic observables, such as work, exhibit bistability in the temporally metastable regime. We demonstrate that the inertial-like Stuart-Landau dimer operates like a machine, reliably outputting the most work when the oscillators coherently synchronize and unreliable with minimum work output when the oscillators are incoherent. Overall, our results show the importance of coherent synchronization within the working substance in the operation of a thermal machine.