III. Ecosmos: A Revolutionary Fertile, Habitable, Solar-Bioplanet, Incubator Lifescape

D. Non-Equilibrium Thermodynamics of Living Systems

Wolfram, Stephen. The Second Law: Resolving the Mystery of the Second Law of Thermodynamics. Online: Wolfram Media, 2023. Since the 1980s, the polymath philosopher and software designer has developed a cellular automata computational method which has gained a wide and deep applicability. For his whole scale achievements, please visit his home site at stephenwolfram.com. See also his latest edition How Did We Get Here? The Tangled History of the Second Law of Thermodynamics at arXiv:2311.10722.

Ever since it was first formulated a century and a half ago, the Second Law of thermodynamics has an air of mystery about it. In this book, Stephen Wolfram builds on recent breakthroughs in the foundations of physics to propose that it emerges as a general feature of computational processes by virtue of their interplay with our similar activities as observers. In the book, Wolfram tells the story of his own quest as well as trace the whole history of the Second Law. We next sample its Table of Contents.

The Basic Arc of the Story · Heat Engines and the Beginnings of Thermodynamics · The Second Law Is Formulated · The Concept of Entropy · "Deriving" the Second Law from Molecular Dynamics · The Concept of Ergodicity · Maxwell's Demon · Coarse Graining and the "Modern Formulation" · The Second Law and Quantum Mechanics · Continuous Versus Discrete · So Where Does This Leave the Second Law?

A cellular automaton is a collection of cells arranged in a grid of specified shape, such that each cell changes state as a function of time, according to a defined set of rules driven by the states of neighboring cells.

Zenil, Hector, et al. The Thermodynamics of Network Coding, and an Algorithmic Refinement of the Principle of Maximum Entropy. Entropy. 21/6, 2019. This paper by the Karolinska Institute, Stockholm computational theorists HZ, Narsis Kiani and Jesper Tegner is noted by the voluminous online journal site as among its most popular, because readers (like me) sense the authors are indeed closing on brilliant insights, however couched in technicalities, as the Abstract conveys. Something is really going on by itself as we ever try to get a good read and bead upon it, which may well be our cosmic purpose.

The principle of maximum entropy (Maxent) is often used to obtain prior probability distributions as a method to obtain a Gibbs measure under some restriction giving the probability that a system will be in a certain state compared to the rest of the elements. Here we take advantage of a causal algorithmic calculus to derive a thermodynamic-like result based on how difficult it is to reprogram a computer code. Using the distinction between computable and algorithmic randomness, we quantify the cost in information loss associated with reprogramming. To illustrate this, we apply the algorithmic refinement to Maxent on graphs and introduce a generalized Maximal Algorithmic Randomness Preferential Attachment (MARPA) Algorithm. Our study motivates further analysis of the origin and consequences of the aforementioned asymmetries, reprogrammability, and computation. (Abstract excerpt)

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