Oscillations in feedback driven systems: thermodynamics and noise

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.

arXiv comment11 pages, 8figures

References in corpus (19)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Modeling spontaneous breaking of time-translation symmetry
• Nonequilibrium Thermodynamics of Feedback Control
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• The free energy cost of accurate biochemical oscillations
• Thermodynamics of feedback controlled systems
• An allosteric model of KaiC phosphorylation
• Discrete time crystals in the absence of manifest symmetries or disorder in open quantum systems
• Amplified biochemical oscillations in cellular systems
• The fate of a discrete time crystal in an open system
• Coherence of Biochemical Oscillations is Bounded by Driving Force and Network Topology
• Period-doubling in period-$1$ steady states
• The Thermodynamic Uncertainty Relation in Biochemical Oscillations
• Phase transition in thermodynamically consistent biochemical oscillators
• Stochastic thermodynamics of self-oscillations: the electron shuttle
• Quantifying fluctuations in reversible enzymatic cycles and clocks
• Subharmonic oscillations in stochastic systems under periodic driving

Cited by in corpus (7)

• Nonequilibrium Phase Transition To Temporal Oscillations In Mean-Field Spin Models
• Discontinuous phase transition from ferromagnetic to oscillating states in a nonequilibrium mean-field spin model
• Collective oscillations in a three-dimensional spin model with non-reciprocal interactions
• Hidden collective oscillations in a disordered mean-field spin model with non-reciprocal interactions
• Inference of Time-Reversal Asymmetry from Time Series in a Piezoelectric Energy Harvester
• Far-from-equilibrium complex landscapes
• Tailoring the overlap distribution in driven mean-field spin models