Title
Relating The Thermodynamic Arrow Of Time To The Causal Arrow
Keywords
New applications of statistical mechanics
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. © IOP Publishing Ltd.
Publication Date
4-1-2008
Publication Title
Journal of Statistical Mechanics: Theory and Experiment
Volume
2008
Issue
4
Number of Pages
-
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1088/1742-5468/2008/04/P04001
Copyright Status
Unknown
Socpus ID
43049105396 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/43049105396
STARS Citation
Allahverdyan, Armen E. and Janzing, Dominik, "Relating The Thermodynamic Arrow Of Time To The Causal Arrow" (2008). Scopus Export 2000s. 10422.
https://stars.library.ucf.edu/scopus2000/10422