Thermodynamic Depth of Causal States: When Paddling around in Occam's Pool Shallowness Is a Virtue
Skip to main content
eScholarship
Open Access Publications from the University of California

UC Davis

UC Davis Previously Published Works bannerUC Davis

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

  • Author(s): Crutchfield, James P;
  • Shalizi, Cosma Rohilla
  • et al.
Abstract

Thermodynamic 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---$\epsilon$-machines---and show that this representation gives the minimum dive consistent with accurate prediction. Thus, $\epsilon$-machines are optimally shallow.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
For improved accessibility of PDF content, download the file to your device.
Current View