Thermodynamic Depth of Causal States: When Paddling around in Occam's Pool Shallowness Is a Virtue

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dc.creatorCrutchfield, James P.
dc.creatorShalizi, Cosma Rohilla
dc.date1998-08-13
dc.date.accessioned2026-07-07T03:11:18Z
dc.date.available2026-07-07T03:11:18Z
dc.descriptionThermodynamic depth is an appealing but flawed structural complexity measure. It depends on a set of macroscopic states for a system, but neither its original introduction by Lloyd and Pagels nor any follow-up work has considered how to select these states. Depth, therefore, is at root arbitrary. Computational mechanics, an alternative approach to structural complexity, provides a definition for a system's minimal, necessary causal states and a procedure for finding them. We show that the rate of increase in thermodynamic depth, or {\it dive}, is the system's reverse-time Shannon entropy rate, and so depth only measures degrees of macroscopic randomness, not structure. To fix this we redefine the depth in terms of the causal state representation---$ε$-machines---and show that this representation gives the minimum dive consistent with accurate prediction. Thus, $ε$-machines are optimally shallow.
dc.description11 pages, 9 figures, RevTeX
dc.identifierhttps://arxiv.org/abs/cond-mat/9808147
dc.identifierhttp://arxiv.org/abs/cond-mat/9808147
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/28522
dc.subjectStatistical Mechanics
dc.subjectAdaptation and Self-Organizing Systems
dc.subjectChaotic Dynamics
dc.titleThermodynamic Depth of Causal States: When Paddling around in Occam's Pool Shallowness Is a Virtue
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