Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference

2015/12/07 by Dominik Janzing, Rafael Chaves, Bernhard Schölkopf +1
Arts and Humanities · Mathematics · Neuroscience · Physics and Astronomy · Psychology · #Arrow of time #Asymmetry #Causal inference #Conditional independence #Distribution (mathematics) #Embodied and Extended Cognition #Field (mathematics) #Independence (probability theory) #Initial value problem #Philosophy and History of Science #Philosophy and Theoretical Science #Second law of thermodynamics #cond-mat.stat-mech #math.ST #quant-ph #stat.TH

paper · pdf · doi:10.1088/1367-2630/18/9/093052

published as New J. Phys. 18, 093052 (2016) · 7 pages, latex, 2 figures

arxiv created 2015/12/07 · openalex created_date 2016/06/24 · openalex publication_date 2016/09/27 · arxiv updated 2016/11/08 · openalex updated_date 2026/08/06

Abstract

We postulate a principle stating that the initial condition of a physical system is typically algorithmically independent of the dynamical law. We discuss the implications of this principle and argue that they link thermodynamics and causal inference. On the one hand, they entail behavior that is similar to the usual arrow of time. On the other hand, they motivate a statistical asymmetry between cause and effect that has recently been postulated in the field of causal inference, namely, that the probability distribution contains no information about the conditional distribution and vice versa, while may contain information about .

Citations

• A Theory of Program Size Formally Identical to Information Theory
• Reduced Dynamics Need Not Be Completely Positive
• Gibbs vs Boltzmann Entropies
• The thermodynamics of computation—a review
• Bell nonlocality