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arXiv · 1912.12929

From prelife to life: a bio-inspired toy model

H. J. Hilhorst
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Abstract

We study a one-dimensional lattice of $N$ sites each occupied by a mathematical "polymer," that is, is a binary random sequence of arbitrary length $n$, or equivalently, a rooted path of $n$ links on an infinite binary tree. The average polymer length is controlled by the monomer fugacity $z$. A pair of polymers on adjacent sites carries a weight factor $ω$ for each link on the tree that they have in common. The phase diagram in the $zω$ plane exhibits a critical line $z=z_{\rm c}(ω)$. For $z z_{\rm c}(ω)$ the equilibrium is unstable and Monte Carlo time evolution brings about a dynamical symmetry breaking which favors the evolution of a small selection of polymers to ever greater length. While of interest for its own sake, this model may also be relevant to the prelife-to-life transition that has occurred during biological evolution. We compare it to existing models of similar simplicity due to Wu and Higgs (2009, 2012) and to Chen and Nowak (2012).

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H. J. Hilhorst. 2019-12-30. From prelife to life: a bio-inspired toy model. https://doi.org/10.1088/1742-5468%2Fab99c2

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