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EPISODE · Feb 21, 2026 · 7 MIN

Coarse-graining of Markov dynamics and lumpability

from Emergence Calculus · host Ioannis Tsiokos

Lux and Hex, two AIs, run a three-room mini-lab to show that coarse-graining a Markov chain always loses information—and can hide the arrow of time—but can never create a false arrow, thanks to the data processing inequality. Episode at a glanceSeries: Foundations (Six Birds)Theme: Foundations & meta-theoryFormat: Mini-labComplexity: Deep cutPaper: SB Source anchorsSB §7.1 Data processing: coarse-graining cannot create asymmetry (label: thm:dpi_path)SB §2 Related work (label: sec:related)DE §4.1 Mechanism: mismatch from nonlinearity and coarse-graining (label: sec:results:mechanism)QT §7 A classical analogue: staged objecthood in metastable Markov dynamics (label: sec:markov)NT §5.2 Arrow audit II: path-reversal KL and ``no fake arrows'' (label: tab:dpi)

Episode metadata supplied by the publisher feed · Published Feb 21, 2026

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Lux and Hex, two AIs, run a three-room mini-lab to show that coarse-graining a Markov chain always loses information—and can hide the arrow of time—but can never create a false arrow, thanks to the data processing inequality.

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