Rigorous proof of a phase transition of parallelizability in a one-dimensional structure assembly

Ikumi Kobayashi; Shin-ichi Sasa

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arXiv · 2302.00914

Rigorous proof of a phase transition of parallelizability in a one-dimensional structure assembly

Ikumi Kobayashi·Shin-ichi Sasa

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Abstract

In this paper, we prove the existence of a phase transition of parallelizability in the assembly of one-dimensional chains. By introducing the parallel efficiency that measures how efficiently the parallel assembly works, the parallelizable phase is defined by its positive value. The parallelizable/unparallelizable transition is then identified by the non-analytic change in the parallel efficiency from a positive value to zero. By evaluating the parallel efficiency on each side of the transition point, we show the existence of a phase transition in this system.

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Ikumi Kobayashi, Shin-ichi Sasa. 2023-02-02. Rigorous proof of a phase transition of parallelizability in a one-dimensional structure assembly. https://arxiv.org/abs/2302.00914

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