Oscillations in feedback driven systems: thermodynamics and noise

TL;DR

This paper systematically investigates oscillations in feedback driven nonequilibrium systems using stochastic thermodynamics, revealing their relation to thermodynamic cost, noise, and phase transitions, with insights into coherence and entropy production.

Contribution

It introduces a comprehensive analysis of feedback driven oscillations, including a simple two-state model and a complex Ising model, highlighting thermodynamic and informational aspects.

Findings

Oscillations can be coherent indefinitely with diverging thermodynamic cost.

Feedback driven Ising model exhibits subharmonic oscillations similar to time-crystals.

Total entropy change remains positive when including informational contributions.

Abstract

Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically driven systems such as time-crystals. Oscillations in autonomous systems and, to a lesser degree, subharmonic oscillations in periodically driven systems have been both thoroughly investigated, including their relation with thermodynamic cost and noise. We perform a systematic study of oscillations in a third class of nonequilibrium systems: feedback driven systems. In particular, we use the apparatus of stochastic thermodynamics to investigate the role of noise and thermodynamic cost in feedback driven oscillations. For a simple two-state model that displays oscillations, we analyze the relation between precision and dissipation, revealing that oscillations can remain coherent for an indefinite time in a finite system with thermal fluctuations in a limit of diverging thermodynamic cost. We consider oscillations in a more complex system with several degrees of freedom, an Ising model driven by feedback between the magnetization and the external field. This feedback driven system can display subharmonic oscillations similar to the ones observed in time-crystals. We illustrate the second law for feedback driven systems that display oscillations. For the Ising model, the oscillating dissipated heat can be negative. However, when we consider the total entropy that also includes an informational term related to measurements, the oscillating total entropy change is always positive. We also study the finite-size scaling of the dissipated heat, providing evidence for the existence of a first-order phase transition for certain parameter regimes.