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  Relating the Thermodynamic Arrow of Time to the Causal Arrow

Allahverdyan, A., & Janzing, D. (2008). Relating the Thermodynamic Arrow of Time to the Causal Arrow. Journal of Statistical Mechanics: Theory and Experiment, 2008: P04001, pp. 1-21. doi:10.1088/1742-5468/2008/04/P04001.

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Allahverdyan, AE, Author
Janzing, D1, Author              
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 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.

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 Dates: 2008-04
 Publication Status: Published in print
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 Identifiers: DOI: 10.1088/1742-5468/2008/04/P04001
BibTex Citekey: 5391
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Title: Journal of Statistical Mechanics: Theory and Experiment
Source Genre: Journal
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Publ. Info: Bristol, England : Institute of Physics Publishing
Pages: - Volume / Issue: 2008 Sequence Number: P04001 Start / End Page: 1 - 21 Identifier: ISSN: 1742-5468
CoNE: https://pure.mpg.de/cone/journals/resource/111076098244006