  The circadian oscillator exhibits remarkably high temporal precision, despite
its exposure to several fluctuations. The central mechanism that protects the
oscillator from 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 linearized
Kuramoto model by using stochastic thermodynamics. For general coupling, we
find that the temporal precision is bounded from below by the information flow.
We generalize the model to incorporate a time-delayed coupling and demonstrate
that the same relation also holds for the time-delayed case. Furthermore, the
temporal precision is demonstrated to be improved in the presence of the time
delay, and we show that the increased information flow is responsible for the
time-delay-induced precision improvement.
