Relating the thermodynamic arrow of time to the causal arrow

    Authors

    A. E. Allahverdyan;D. Janzing

    Comments

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    Abbreviated Journal Title

    J. Stat. Mech.-Theory Exp.

    Keywords

    new applications of statistical mechanics; QUANTUM SYSTEMS; 2ND-LAW; ENTROPY; THEOREM; CHAOS; GIBBS; PROOF; Mechanics; Physics, Mathematical

    Abstract

    Consider a Hamiltonian system that consists of a slow subsystem S and a fast subsystem F. The autonomous dynamics of S is driven by an effective Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined thermodynamic arrow of time (second law) emerges for S whenever there is a well-defined causal arrow from S to F and the back-action is negligible. This is because the back-action of F on S is described by a non-globally Hamiltonian Born Oppenheimer term that violates the Liouville theorem, and makes the second law inapplicable to S. If S and F are mixing, under the causal arrow condition they are described by microcanonical distributions P(S) and P(S|F). Their structure supports a causal inference principle proposed recently in machine learning.

    Journal Title

    Journal of Statistical Mechanics-Theory and Experiment

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    21

    WOS Identifier

    WOS:000255662000005

    ISSN

    1742-5468

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