The thermodynamics of clocks

TL;DR

This paper explores the thermodynamic principles governing all types of clocks, highlighting how energy dissipation and noise fundamentally limit their accuracy and performance, with implications for classical and quantum systems.

Contribution

It provides a unified thermodynamic framework for understanding classical and quantum clocks, emphasizing the role of energy dissipation and measurement in clock performance.

Findings

Good clocks require large energy dissipation.

Phase diffusion limits periodic clock accuracy.

Measurement and low entropy reservoirs are crucial for quantum clocks.

Abstract

All clocks, classical or quantum, are open non equilibrium irreversible systems subject to the constraints of thermodynamics. Using examples I show that these constraints necessarily limit the performance of clocks and that good clocks require large energy dissipation. For periodic clocks, operating on a limit cycle, this is a consequence of phase diffusion. It is also true for non periodic clocks (for example, radio carbon dating) but due to telegraph noise not to phase diffusion. In this case a key role is played by accurate measurements that decrease entropy, thereby raising the free energy of the clock, and requires access to a low entropy reservoir. In the quantum case, for which thermal noise is replaced by quantum noise (spontaneous emission or tunnelling), measurement plays an essential role for both periodic and non periodic clocks. The paper concludes with a discussion of the Tolman relations and Rovelli's thermal time hypothesis in terms of clock thermodynamics.