Life at the boundary of chemical kinetics and program execution.

Abstract

This work introduces a generic quantitative framework for studying dynamical processes that involve interactions of polymer sequences. Possible applications range from quantitative studies of the reaction kinetics of polymerization processes to explorations of the behavior of chemical implementations of computational-including basic lifelike-processes. This way, we establish a bridge between thermodynamic and computational aspects of systems that are defined in terms of sequence interactions. As by-products of these investigations, we clarify some common confusion around the notion of "autocatalysis" and show quantitatively how a chemically implemented Turing machine can operate close to the Landauer bound. Using a Markov process model of polymer sequence composition and dynamical evolution of the Markov process's parameters via an ordinary differential equation that arises when taking the double "chemical" many-particle limit as well as "rarefied interactions" limit, this approach enables-for example-accurate quantitative explorations of entropy generation in systems where computation is driven by relaxation to thermodynamic equilibrium. The computational framework internally utilizes the Scheme programming language's intrinsic continuation mechanisms to provide nondeterministic evaluation primitives that allow the user to specify example systems in straight purely functional code, making exploration of all possible relevant sequence composition constellations-which would be otherwise tedious to write code for-automatic and hidden from the user. As the original motivation for this work came from investigations into emergent program evolution that arises in computational substrates of the form discussed in recent work on "computational life" [Alakuijala et al. arXiv:2406.19108], a major focus of attention is on giving a deeper explanation of key requirements for the possible emergence of self-replicators, especially in settings whose behavior is governed by real-world physics rather than ad hoc rules that may be difficult to implement in a physical system. A collection of fully worked out examples elucidate how this modeling approach is quantitatively related to Monte Carlo-based simulations, as well as exact or approximate analytic approaches, and how it can be utilized to study a broad range of different systems. These examples can also serve as starting points for further explorations.