Information dynamics and the arrow of time

TL;DR

This paper introduces a stochastic cellular automaton model derived from reversible dynamics to explain the emergence of the arrow of time, linking information processing, thermodynamics, and entropy concepts.

Contribution

It develops a novel stochastic PCA model from reversible cellular automata to analyze time asymmetry and information laws in physical and computational systems.

Findings

SPCAs satisfy generalized second law of thermodynamics

The model demonstrates emergent time-reversal asymmetry

Algorithmic entropy is conceptually primary over other entropies

Abstract

Why does time appear to pass irreversibly? To investigate, we introduce a class of partitioned cellular automata (PCAs) whose cellwise evolution is based on the chaotic baker's map. After imposing a suitable initial condition and restricting to a macroscopic view, we are left with a stochastic PCA (SPCA). When the underlying PCA's dynamics are reversible, the corresponding SPCA serves as a model of emergent time-reversal asymmetry. Specifically, we prove that its transition probabilities are homogeneous in space and time, as well as Markov relative to a Pearlean causal graph with timelike future-directed edges. Consequently, SPCAs satisfy generalizations of the second law of thermodynamics, which we term the Resource and Memory Laws. By subjecting information-processing agents (e.g., human experimenters) to these laws, we clarify issues regarding the Past Hypothesis, Landauer's principle, Boltzmann brains, scientific induction, and the so-called psychological arrow of time. Finally, by describing a theoretical agent powered by data compression, we argue that the algorithmic entropy takes conceptual precedence over both the Shannon-Gibbs and Boltzmann entropies.