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.

Oscillations Governed by the Incoherent Dynamics in Necroptotic Signaling

“…Numerous studies have explored the design principle of signaling circuits with various biological functions. The relationships between network motifs [26] (such as paradoxical components [27][28][29], feed-forward loop [30], and feedback loop [31][32][33]) and biochemical oscillator [34][35][36], adaptation [37], robustness [38][39][40][41], and noise attenuation [42][43][44] have been revealed successively. Designing and developing a signaling circuit system with regulatory function is of guiding significance for the further understanding of how oscillation signals regulate biological processes [13,45].…”

Inference of Time-Reversal Asymmetry from Time Series in a Piezoelectric Energy Harvester

“…The energy harvester and the related model considered in our paper represent an instance of non-Markovian systems, where feedback mechanisms and memory effects are at play. These kinds of models have been the object of an intense study in recent years, from the point of view of stochastic thermodynamics [23][24][25][26][27][28][29][30][31].…”

Epidemic oscillations induced by social network control

“…The modeling of containment measures in compartmentalized epidemic models [6] is thus under the focus of intense research [7,8]. It has been very recently rigorously demonstrated that compartimentalized epidemic models display oscillations in presence of feedback between infection rate and infection states [9],and that in general a feedback between order and control parameters in large interacting systems subject to phase transitions triggers self-oscillations [10,11], where an Andronov-Hopf bifurcation takes over the usual phase transition. As infection and recovery rates are changed, epidemic models on networks display out-of-equilibrium phase transitions between a phase where a disease is prevented from spreading and a phase where a finite fraction of the population becomes infected [12].…”