The First Law of Complexodynamics

This post explores why physical systems’ “complexity” rises, peaks, then falls over time, unlike entropy, which always increases. Using Kolmogorov complexity and the notion of “sophistication,” the author proposes a formal way to capture this pattern, introducing the idea of “complextropy” — a complexity measure that’s low in both highly ordered and fully random states but peaks during intermediate, evolving phases. He suggests using computational resource bounds to make the measure meaningful and proposes both theoretical and empirical (e.g., using file compression) approaches to test this idea, acknowledging it as an open problem.

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Introduction

A few weeks ago, I had the pleasure of attending FQXi’s Setting Time Aright conference, part of which took place on a cruise from Bergen, Norway to Copenhagen, Denmark. (Why aren’t theoretical computer science conferences ever held on cruises? If nothing else, it certainly cuts down on attendees sneaking away from the conference venue.) This conference brought together physicists, cosmologists, philosophers, biologists, psychologists, and (for some strange reason) one quantum complexity blogger to pontificate about the existence, directionality, and nature of time. If you want to know more about the conference, check out Sean Carroll’s Cosmic Variance posts here and here

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Websitescottaaronson.blog
Published date2011/09/23

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