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

Socpus ID

43049105396 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/43049105396

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