Dissipation and fluctuations of CMOS ring oscillators close to criticality

Abstract

We analyze a thermodynamically consistent model of CMOS-based ring oscillators near the onset of coherent voltage oscillations. For driving voltages close to the critical value, we derive the normal form of the Hopf bifurcation that underlies the oscillation transition in the thermodynamic limit. Using this normal form, we determine the phase and amplitude dynamics, and demonstrate that entropy dissipation decreases in the oscillating state for ring oscillators with more than three inverters. These findings culminate in a stability-dissipation relation, which links the observed decrease in dissipation to an increase in the local stability of the oscillating state. Next, we characterize finite-size fluctuations of the amplitude and phase near the critical voltage, using a stochastic version of the normal form. We demonstrate that close to the transition, finite-size fluctuations remain important at arbitrary system size, introducing oscillations even below the critical voltage. We further show that these noise-induced oscillations have an anomalously short decoherence time that scales sub-linearly with the system-size, in contrast to the behavior far from criticality.

arXiv comment14 pages, 7 figures

References in corpus (17)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Predator-prey cycles from resonant amplification of demographic stochasticity
• Ensemble and Trajectory Thermodynamics: A Brief Introduction
• Cost and Precision of Brownian Clocks
• How limit cycles and quasi-cycles are related in systems with intrinsic noise
• Collective power: Minimal model for thermodynamics of nonequilibrium phase transitions
• Stochastic Thermodynamics of Non-Linear Electronic Circuits: A Realistic Framework for Computing around kT
• Phase transition in thermodynamically consistent biochemical oscillators
• The thermodynamics of clocks
• Macroscopic Stochastic Thermodynamics
• Principles of Low Dissipation Computing from a Stochastic Circuit Model
• Inflow rate, a time-symmetric observable obeying fluctuation relations
• Self-excited oscillation and synchronization of an on-fiber optomechanical cavity
• Design principles for biochemical oscillations with limited energy resources
• Minimum-dissipation principle for synchronised stochastic oscillators far from equilibrium
• Stochastic thermodynamic bounds on logical circuit operation
• Small-amplitude synchronisation in driven Potts models