Subharmonic oscillations in stochastic systems under periodic driving

Abstract

Subharmonic response is a well known phenomena in, e.g., deterministic nonlinear dynamical systems. We investigate the conditions under which such subharmonic oscillations can persist for a long time in open systems with stochastic dynamics due to thermal fluctuations. In contrast to stochastic autonomous systems in a stationary state, for which the number of coherent oscillations is fundamentally bounded by the number of states in the underlying network, we demonstrate that in periodically driven systems, subharmonic oscillations can, in principle, remain coherent forever, even in networks with a small number of states. We also show that, {\sl inter alia}, the thermodynamic cost rises only logarithmically with the number of coherent oscillations in a model calculation and that the possible periods of the persistent subharmonic response grow linearly with the number of states. We argue that our results can be relevant for biochemical oscillations and for stochastic models of time-crystals.

arXiv comment7 pages, 6 figures

References in corpus (30)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Observation of a Discrete Time Crystal
• Observation of discrete time-crystalline order in a disordered dipolar many-body system
• Floquet Time Crystals
• On the phase structure of driven quantum systems
• Efficiency at maximum power: An analytically solvable model for stochastic heat engines
• Many-body localization in periodically driven systems
• Brownian Carnot engine
• Fate of many-body localization under periodic driving
• Modeling spontaneous breaking of time-translation symmetry
• Phototaxis of synthetic microswimmers in optical landscapes
• Equilibration and Order in Quantum Floquet Matter
• Discrete Time-Crystalline Order in Cavity and Circuit QED Systems
• A theory of many-body localization in periodically driven systems
• The free energy cost of accurate biochemical oscillations
• The Einstein relation generalized to non-equilibrium
• Cost and Precision of Brownian Clocks
• Engineered swift equilibration of a Brownian particle
• Thermodynamics of Micro- and Nano-Systems Driven by Periodic Temperature Variations
• 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
• Mimicking Nonequilibrium Steady States with Stochastic Pumps
• Quantifying fluctuations in reversible enzymatic cycles and clocks
• Chemical event chain model of coupled genetic oscillators
• Feedback traps for virtual potentials

Cited by in corpus (9)

• Discrete Time Crystals
• Thermodynamic Bound on the Asymmetry of Cross-Correlations
• Classical Stochastic Discrete Time Crystals
• Stochastic discrete time crystals: Entropy production and subharmonic synchronization
• Stochastic thermodynamics of chemical reactions coupled to finite reservoirs: A case study for the Brusselator
• Oscillations in feedback driven systems: thermodynamics and noise
• Oscillating states of periodically driven anharmonic Langevin systems
• Extreme-Value Statistics of Stochastic Transport Processes: Applications to Molecular Motors and Sports
• Oscillating states of driven Langevin systems in large viscous regime