Moore’s Clock

• Published in: Physica A Vol. 541; p. 123619
• Main Authors: Eliazar, Iddo, Shlesinger, Michael F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2020
• Subjects: Exponential distribution; Gompertz distribution; Gumbel distribution; Harmonic series; Poisson processes; Zipf’s Law; Harmonic series; Gompertz distribution; Gumbel distribution; Zipf’s Law; Exponential distribution; Poisson processes
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2019.123619

Considering a stochastic clock – a chronograph that ticks randomly according to an underpinning ticking rate – we address the durations between its successive ticking epochs and ask: when are the inter-ticking durations independent of each other? We establish that this question has two answers: equilibrium and non-equilibrium. The equilibrium answer is termed Benchmark Clock, it is characterized by a constant ticking rate, and it corresponds to the time-flow of a “steady-state universe” model. The non-equilibrium answer is termed Moore’s Clock, it is characterized by an exponential ticking rate, and it corresponds to the time-flow of a “big-bang universe” model. In the context of stochastic clocks, Moore’s Clock is the manifestation of Moore’s Law of accelerating change . This paper explores the rich statistical structure of Moore’s Clock, and pinpoints the dramatic differences between the stationary Benchmark Clock and the non-stationary Moore’s Clock. •Clocks that tick randomly over the real line are considered.•Only two such clocks have independent inter-ticking durations.•The two clocks are characterized by constant and exponential ticking rates.•We term the latter “Moore’s Clock” and explore its rich temporal structure.