Modeling the Arrows of Time with Causal Multibaker Maps

Aram Ebtekar*, Marcus Hutter

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)

    Abstract

    Why do we remember the past, and plan the future? We introduce a toy model in which to investigate emergent time asymmetries: the causal multibaker maps. These are reversible discrete-time dynamical systems with configurable causal interactions. Imposing a suitable initial condition or “Past Hypothesis”, and then coarse-graining, yields a Pearlean locally causal structure. While it is more common to speculate that the other arrows of time arise from the thermodynamic arrow, our model instead takes the causal arrow as fundamental. From it, we obtain the thermodynamic and epistemic arrows of time. The epistemic arrow concerns records, which we define to be systems that encode the state of another system at another time, regardless of the latter system’s dynamics. Such records exist of the past, but not of the future. We close with informal discussions of the evolutionary and agential arrows of time, and their relevance to decision theory.

    Original languageEnglish
    Article number776
    Number of pages19
    JournalEntropy
    Volume26
    Issue number9
    DOIs
    Publication statusPublished - Sept 2024

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