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 |
| Bibtex Type: | Article (article) |
| DOI: | 10.1088/1742-5468/2008/04/P04001 |
| Digital: | 0 |
| Electronic Archiving: | grant_archive |
| Language: | en |
| Organization: | Max-Planck-Gesellschaft |
| School: | Biologische Kybernetik |
| Links: | |
BibTex
@article{5391,
title = {Relating the Thermodynamic Arrow of Time to the Causal Arrow},
journal = {Journal 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 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.},
volume = {2008},
number = {P04001},
pages = {1-21},
organization = {Max-Planck-Gesellschaft},
school = {Biologische Kybernetik},
month = apr,
year = {2008},
slug = {5391},
author = {Allahverdyan, AE. and Janzing, D.},
month_numeric = {4}
}