Moore’s Clock

Iddo Eliazar and Michael F. Shlesinger

Physica A: Statistical Mechanics and its Applications, 2020, vol. 541, issue C

Abstract: 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.

Keywords: Poisson processes; Harmonic series; Zipf’s Law; Exponential distribution; Gumbel distribution; Gompertz distribution (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119320187

DOI: 10.1016/j.physa.2019.123619

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