Thermodynamics of collective enhancement of precision.

The circadian oscillator exhibits remarkably high temporal precision, despite its exposure to several fluctuations. The central mechanism that protects the oscillator from the fluctuations is a collective enhancement of precision, where a population of coupled oscillators displays higher temporal precision than that achieved without coupling. Since coupling is essentially information exchange between oscillators, we herein investigate the relation between the temporal precision and the information flow between oscillators in the Kuramoto model by using stochastic thermodynamics. For general coupling, we find that the temporal precision is bounded from below by the information flow. Explicit calculations of the temporal variance and the information flow are presented for a global uniform coupling model. We generalize the model to incorporate a time-delayed coupling and demonstrate that the same relation also holds for the time-delayed case. Furthermore, we find that the temporal precision is improved in the presence of the time delay and show that the increased information flow is responsible for the time-delay-induced improvement.