Abstract
A major conceptual step forward in understanding the logical architecture of living systems was advanced by von Neumann with his universal constructor, a physical device capable of self-reproduction. A necessary condition for a universal constructor to exist is that the laws of physics permit physical universality, such that any transformation (consistent with the laws of physics and availability of resources) can be caused to occur. While physical universality has been demonstrated in simple cellular automata models, so far these have not displayed a requisite feature of life—namely open-ended evolution—the explanation of which was also a prime motivator in von Neumann’s formulation of a universal constructor. Current examples of physical universality rely on reversible dynamical laws, whereas it is well-known that living processes are dissipative. Here we show that physical universality and open-ended dynamics should both be possible in irreversible dynamical systems if one entertains the possibility of state-dependent laws. We demonstrate with simple toy models how the accessibility of state space can yield open-ended trajectories, defined as trajectories that do not repeat within the expected Poincaré recurrence time and are not reproducible by an isolated system. We discuss implications for physical universality, or an approximation to it, as a foundational framework for developing a physics for life.
Highlights
Schrödinger’s seminal 1943 lectures titled “What is life?” [1] laid out a compelling challenge for physicists to explain the properties of living matter from what we know of physics
We show reversibility is necessary for physical universality only if the dynamical laws do not evolve in time, permitting the possibility of physical universality in irreversible dynamical systems
Following our setup in [12], we study a cellular automata (CA) composed of two coupled subsystems, each using local update rules drawn from the set of Elementary Cellular Automata (ECA)
Summary
Schrödinger’s seminal 1943 lectures titled “What is life?” [1] laid out a compelling challenge for physicists to explain the properties of living matter from what we know of physics. Von Neumann set out to determine the architecture of natural and artificial self-reproducing automata based again on logic combined with consideration of simple physical constraints (such as the finiteness of available resources and available time) [2] He showed that self-reproduction is logically possible for a constructor, which he defined as a machine capable of being programed to perform physical transformations, including transforming available resources to produce a copy of itself. In addition to the more obvious universal limitations including the finiteness of resources and constraints imposed by the laws of physics, a self-reproducing constructor is limited in its ability to reproduce by two additional constraints: the physical transformations it can perform and the number of programs containing its specification. He stopped short of solving the harder problem of how such a device could follow from physical principles (this harder problem was recently advanced byMarletto in [5] within the formalism of Constructor theory)
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