Relating the thermodynamic arrow of time to the causal arrow
By Armen E. Allahverdyan, Dominik Janzing. 2007
7 citations recorded by the source corpus.
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.
Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics
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In Atomic and Molecular Physics, and Optics
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Citations in the corpus
- Algorithmic independence of initial condition and dynamical law in thermodynamics and causal inference (2015, background): “logp(xjy) 1 X @2 @x@y p(xjy): 1The dicult question how well-dened causal directions emerge in physical systems where interactions actually imply mutual in uence is discussed for a toy model in Ref. [49]. 2Note that two variables Z;Ware called statistically independent if p() = Z) W), which is strong”
- On the Entropy Production of Time Series with Unidirectional Linearity (2009, result): “Some first explanations were provided by observations in [28, 29 ].”