Thermodynamics of collective enhancement of precision

TL;DR

This paper explores how coupled oscillators, modeled by the Kuramoto system, achieve higher temporal precision through information flow, with thermodynamic bounds and effects of time delays analyzed.

Contribution

It establishes a fundamental relation between temporal precision and information flow in coupled oscillators, including effects of time delays, using stochastic thermodynamics.

Findings

Temporal precision is bounded by information flow.

Time delays can enhance precision via increased information flow.

The relation holds for both instantaneous and delayed coupling.

Abstract

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.