Thermodynamic depth of causal states: Objective complexity via minimal representations
- Physics Department, University of California, Berkeley, California 94720-7300 (United States)
- Physics Department, University of Wisconsin, Madison, Wisconsin 53706 (United States)
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{close_quote}s minimal, necessary causal states and a procedure for finding them. We show that the rate of increase in thermodynamic depth, or {ital dive}, is the system{close_quote}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{emdash}{epsilon}-machines{emdash}and show that this representation gives the minimum dive consistent with accurate prediction. Thus, {epsilon}-machines are optimally shallow. {copyright} {ital 1999} {ital The American Physical Society}
- OSTI ID:
- 295527
- Journal Information:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, Issue 1; Other Information: PBD: Jan 1999
- Country of Publication:
- United States
- Language:
- English
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