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Relating the Thermodynamic Arrow of Time to the Causal Arrow




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.

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): Empirical Inference
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


  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},
  month_numeric = {4}