Information dynamics and the arrow of time

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.