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Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton

Aaronson, Scott and Carroll, Sean M. and Ouellette, Lauren (2014) Quantifying the Rise and Fall of Complexity in Closed Systems: The Coffee Automaton. . (Submitted)

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In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Carroll, Sean M.0000-0002-4226-5758
Additional Information:We thank Alex Arkhipov, Charles Bennett, Ian Durham, Dietrich Leibfried, Aldo Pacchiano, and Luca Trevisan for helpful discussions.
Group:Walter Burke Institute for Theoretical Physics
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Record Number:CaltechAUTHORS:20150316-131020808
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55794
Deposited By: Joy Painter
Deposited On:16 Mar 2015 21:20
Last Modified:02 Jun 2023 00:20

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