Life at the Boundary of Chemical Kinetics and Program Execution
Abstract
Abstract
This work introduces a generic quantitative framework for studying
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 life-like
- processes. This way, we establish a bridge between thermodynamic and
computational aspects of systems that are defined in terms of sequence
interactions. As a by-product of these investigations, we clarify some
common confusion around the notion of ``autocatalysis''.
Using a Markov process model of polymer sequence composition and
dynamical evolution of the Markov process's parameters via an ODE 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''
\cite{alakuijala2024computational}, 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 Metropolis 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.
This work introduces a generic quantitative framework for studying
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 life-like
- processes. This way, we establish a bridge between thermodynamic and
computational aspects of systems that are defined in terms of sequence
interactions. As a by-product of these investigations, we clarify some
common confusion around the notion of ``autocatalysis''.
Using a Markov process model of polymer sequence composition and
dynamical evolution of the Markov process's parameters via an ODE 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''
\cite{alakuijala2024computational}, 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 Metropolis 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.
