Thermodynamic depth of causal states: Objective complexity via minimal representations
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 followup 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 dive, is the system's reversetime 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∊machinesand show that this representation gives the minimum dive consistent with accurate prediction. Thus, ∊machines are optimally shallow.
 Publication:

Physical Review E
 Pub Date:
 January 1999
 DOI:
 10.1103/PhysRevE.59.275
 Bibcode:
 1999PhRvE..59..275C
 Keywords:

 05.20.y;
 05.45.a;
 05.70.Ce;
 Classical statistical mechanics;
 Nonlinear dynamics and chaos;
 Thermodynamic functions and equations of state