Effective Theories for Circuits and Automata

TL;DR

This paper develops a framework for constructing effective theories of complex systems with dissipation, irreversibility, and feedback, revealing how these factors influence emergent structures and their lifetimes.

Contribution

It introduces a method to derive effective theories in irreversible, noisy systems using Krohn-Rhodes theorem, highlighting the impact of dissipation on emergent structures.

Findings

Irreversibility and noise limit the lifetimes of emergent structures.

Feedback mechanisms can lead to novel effective behaviors.

Group properties may be enriched temporarily despite dissipation.

Abstract

Abstracting an effective theory from a complicated process is central to the study of complexity. Even when the underlying mechanisms are understood, or at least measurable, the presence of dissipation and irreversibility in biological, computational and social systems makes the problem harder. Here we demonstrate the construction of effective theories in the presence of both irreversibility and noise, in a dynamical model with underlying feedback. We use the Krohn-Rhodes theorem to show how the composition of underlying mechanisms can lead to innovations in the emergent effective theory. We show how dissipation and irreversibility fundamentally limit the lifetimes of these emergent structures, even though, on short timescales, the group properties may be enriched compared to their noiseless counterparts.