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arXiv:1405.6903cond-mat.stat-mech

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

Scott Aaronson, Sean M. Carroll, Lauren Ouellette

Abstract

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.

arXiv comments
22 pages, lots of figures
Journal reference
DOI
Subjects
cond-mat.stat-mechStatistical Mechanics gr-qcGeneral Relativity and Quantum Cosmology nlin.CGCellular Automata and Lattice Gases

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Linked by 5 identifiable commenters in 5 comments across 4 threads, from May 2024 to Jul 2026. Found in 1 HN submission from Jun 2020 to Jun 2020. Open submission discussions.

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Discussed in comments4 threads

  1. 30papers.com – Ilya's 30 essential ML papers, in a beginner friendly format 2 comments

    • https://colah.github.io/posts/2015-08-Understanding-LSTMs/ https://papers.nips.cc/paper/2012/hash/c399862d3b9d6b76c8436... https://papers.nips.cc/paper_files/paper/2012/file/c399862d3... https://arxiv.org/pdf/1512.03385 https://arxiv.org/pdf/1511.07122…

      gooobView on HNParent context

    • No need stupid moving texts. CS231n: Convolutional Neural Networks for Visual Recognition - https://cs231n.github.io/ The Unreasonable Effectiveness of Recurrent Neural Networks - https://karpathy.github.io/2015/05/21/rnn-effectiveness/ Understanding LSTM Networks…

      cute_boiView on HNParent context

  2. What Is Entropy? 1 comment

    • By Jeeves, it's rentropy!! Sean and Stephen are absolutely thoughtful popularizers, but complexity, not entropy, is what they are truly interested in talking about. Although it doesn't make complexity less scary, here's something Sean's been working on for more than a decade.…

      gsf_emergencyView on HNParent context

  3. Why Everything in the Universe Turns More Complex 1 comment

    • Sean Carroll today's go-to person for GR has been working at popularizing these ideas (for more than 10 years(!)) https://arxiv.org/abs/1405.6903 >For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and…

      gsf_emergency_2View on HNParent context

  4. Ilya Sutskever: “If you learn all of these, you’ll know 90% of what matters” 1 comment

    • a backup just in case https://nlp.seas.harvard.edu/annotated-transformer/ https://scottaaronson.blog/?p=762 https://karpathy.github.io/2015/05/21/rnn-effectiveness/ https://colah.github.io/posts/2015-08-Understanding-LSTMs/ https://arxiv.org/pdf/1409.2329.pdf…

      is_trueView on HNParent context

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