Relating the Thermodynamic Arrow of Time to the Causal Arrow
2008
Article
ei
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 BornOppenheimer 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.
Author(s): | Allahverdyan, AE. and Janzing, D. |
Journal: | Journal of Statistical Mechanics |
Volume: | 2008 |
Number (issue): | P04001 |
Pages: | 1-21 |
Year: | 2008 |
Month: | April |
Day: | 0 |
Department(s): | Empirische Inferenz |
Bibtex Type: | Article (article) |
Digital: | 0 |
DOI: | 10.1088/1742-5468/2008/04/P04001 |
Language: | en |
Organization: | Max-Planck-Gesellschaft |
School: | Biologische Kybernetik |
Links: |
Web
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BibTex @article{5391, title = {Relating the Thermodynamic Arrow of Time to the Causal Arrow}, author = {Allahverdyan, AE. and Janzing, D.}, journal = {Journal of Statistical Mechanics}, volume = {2008}, number = {P04001}, pages = {1-21}, organization = {Max-Planck-Gesellschaft}, school = {Biologische Kybernetik}, month = apr, year = {2008}, doi = {10.1088/1742-5468/2008/04/P04001}, month_numeric = {4} } |