Thermodynamics of complexity and pattern manipulation

TL;DR

This paper introduces a thermodynamic framework for pattern manipulation, demonstrating how minimal heat dissipation devices operate optimally and linking dissipation limits to the pattern's intrinsic crypticity, a measure of informational complexity.

Contribution

It develops a theoretical framework for pattern manipulators, deriving fundamental thermodynamic limits and connecting them to the pattern's crypticity, a novel complexity measure.

Findings

Least heat dissipation achieved by simplest devices

Derived ultimate limits of heat dissipation in pattern manipulation

Linked heat dissipation to pattern crypticity

Abstract

Many organisms capitalize on their ability to predict the environment to maximize available free energy, and reinvest this energy to create new complex structures. This functionality relies on the manipulation of patterns - temporally ordered sequences of data. Here, we propose a framework to describe pattern manipulators -- devices that convert thermodynamic work to patterns or vice versa - and use them to build a 'pattern engine' that facilitates a thermodynamic cycle of pattern creation and consumption. We show that the least heat dissipation is achieved by the provably simplest devices; the ones that exhibit desired operational behaviour while maintaining the least internal memory. We derive the ultimate limits of this heat dissipation, and show that it is generally non-zero and connected with the pattern's intrinsic crypticity - a complexity theoretic quantity that captures the puzzling difference between the amount of information the pattern's past behaviour reveals about its future, and the amount one needs to communicate about this past to optimally predict the future.